Formats: - HTML - YAML - JSON - 2026-07-21T07:00:29.709717
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [3, 2, 4, 2], 'aut_gens': [[167265, 29606670, 131864130, 245419970], [167265, 15210873, 442321936, 245419970], [14926470, 15210873, 60015573, 245419970], [340708470, 427427072, 383201968, 36946503], [340708470, 427427072, 131864130, 245419970]], 'aut_group': '10368.bd', 'aut_hash': 7501325464046845939, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10368, 'aut_permdeg': 48, 'aut_perms': [6333261748170151247379397101807792107478361906718460509809989, 6425926566075662311587714394739769189392980018070586624886128, 2594874863871791810134145702583520901830131244665749372948078, 332935361180815704243733501997502175618076941300232], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 2, 1], [2, 9, 2, 1], [2, 18, 2, 1], [2, 36, 1, 1], [2, 54, 2, 1], [2, 81, 1, 1], [3, 4, 2, 2], [3, 8, 2, 1], [3, 16, 1, 1], [3, 16, 2, 1], [4, 108, 2, 1], [4, 324, 1, 1], [6, 12, 2, 1], [6, 12, 4, 1], [6, 24, 2, 1], [6, 24, 4, 1], [6, 36, 2, 2], [6, 36, 4, 1], [6, 48, 2, 1], [6, 72, 2, 2], [6, 108, 2, 1], [6, 144, 1, 1], [12, 216, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\wr D_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '10368.bd', 'autcentquo_hash': 7501325464046845939, 'autcentquo_nilpotent': False, 'autcentquo_order': 10368, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\wr D_4', 'cc_stats': [[1, 1, 1], [2, 6, 2], [2, 9, 2], [2, 18, 2], [2, 36, 1], [2, 54, 2], [2, 81, 1], [3, 4, 4], [3, 8, 2], [3, 16, 3], [4, 108, 2], [4, 324, 1], [6, 12, 6], [6, 24, 6], [6, 36, 8], [6, 48, 2], [6, 72, 4], [6, 108, 2], [6, 144, 1], [12, 216, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '2592.cm', 'commutator_count': 1, 'commutator_label': '324.169', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 65, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 2], [2, 9, 1, 2], [2, 18, 1, 2], [2, 36, 1, 1], [2, 54, 1, 2], [2, 81, 1, 1], [3, 4, 1, 4], [3, 8, 1, 2], [3, 16, 1, 3], [4, 108, 1, 2], [4, 324, 1, 1], [6, 12, 1, 6], [6, 24, 1, 6], [6, 36, 1, 8], [6, 48, 1, 2], [6, 72, 1, 4], [6, 108, 1, 2], [6, 144, 1, 1], [12, 216, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 537600, 'exponent': 12, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 8], [16, 1, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2592.cm', 'hash': 6952908971992144288, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 2, 4, 2], 'inner_gens': [[167265, 29439589, 295503684, 245419970], [328449, 29606670, 281164389, 245419970], [1498112, 163699712, 131864130, 22392373], [167265, 29606670, 395176320, 245419970]], 'inner_hash': 6952908971992144288, 'inner_nilpotent': False, 'inner_order': 2592, 'inner_split': False, 'inner_tex': 'S_3^2\\wr C_2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 6], [4, 24], [8, 10], [16, 6]], 'label': '2592.cm', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'S3^2wrC2', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 54, 'number_divisions': 54, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 438, 'number_subgroup_classes': 1029, 'number_subgroups': 24844, 'old_label': None, 'order': 2592, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 291], [3, 80], [4, 540], [6, 1248], [12, 432]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[340708470, 427427072, 131864130, 245419970], [167265, 29606670, 120996825, 244304654]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 24], [8, 10], [16, 6]], 'representations': {'PC': {'code': '37432814164892359578174990475578987297335169041003976436514570902348843', 'gens': [1, 2, 4, 5, 7, 9], 'pres': [9, 2, 2, 2, 3, 2, 3, 2, 3, 3, 109, 46, 579, 1740, 165, 48973, 1372, 130, 230, 1319, 65787, 1932, 186, 31120, 1771, 11681, 1034]}, 'Perm': {'d': 12, 'gens': [245419970, 167265, 29606670, 131864130]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3^2\\wr C_2', 'transitive_degree': 12, 'wreath_data': ['72.bg1', '1296.d1', '2592.a1', '2T1'], 'wreath_product': True}
  • gps_conj_classes • Show schema
    • id: 156458079
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 65, 'group_order': 2592, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 156458090
      {'aut_label': '2A', 'centralizer': '6.b1', 'counter': 2, 'group_counter': 65, 'group_order': 2592, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 22392373, 'size': 6}
    • id: 156458101
      {'aut_label': '2A', 'centralizer': '6.b1', 'counter': 3, 'group_counter': 65, 'group_order': 2592, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 36946503, 'size': 6}
    • id: 156458112
      {'aut_label': '2C', 'centralizer': '9.a1', 'counter': 4, 'group_counter': 65, 'group_order': 2592, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 101873059, 'size': 9}
    • id: 156458123
      {'aut_label': '2C', 'centralizer': '9.a1', 'counter': 5, 'group_counter': 65, 'group_order': 2592, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 116443413, 'size': 9}
    • id: 156458129
      {'aut_label': '2E', 'centralizer': '18.e1', 'counter': 6, 'group_counter': 65, 'group_order': 2592, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 21410, 'size': 18}
    • id: 156458130
      {'aut_label': '2E', 'centralizer': '18.e1', 'counter': 7, 'group_counter': 65, 'group_order': 2592, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 116427189, 'size': 18}
    • id: 156458131
      {'aut_label': '2G', 'centralizer': '36.v1', 'counter': 8, 'group_counter': 65, 'group_order': 2592, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 42030622, 'size': 36}
    • id: 156458132
      {'aut_label': '2H', 'centralizer': '54.b1', 'counter': 9, 'group_counter': 65, 'group_order': 2592, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 271432903, 'size': 54}
    • id: 156458080
      {'aut_label': '2H', 'centralizer': '54.b1', 'counter': 10, 'group_counter': 65, 'group_order': 2592, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 198054903, 'size': 54}
    • id: 156458081
      {'aut_label': '2J', 'centralizer': '81.a1', 'counter': 11, 'group_counter': 65, 'group_order': 2592, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 189505314, 'size': 81}
    • id: 156458082
      {'aut_label': '3A', 'centralizer': '4.i1', 'counter': 12, 'group_counter': 65, 'group_order': 2592, 'label': '3A', 'order': 3, 'powers': [12, 1], 'representative': 15052669, 'size': 4}
    • id: 156458083
      {'aut_label': '3A', 'centralizer': '4.i1', 'counter': 13, 'group_counter': 65, 'group_order': 2592, 'label': '3B', 'order': 3, 'powers': [13, 1], 'representative': 15214597, 'size': 4}
    • id: 156458084
      {'aut_label': '3C', 'centralizer': '4.g1', 'counter': 14, 'group_counter': 65, 'group_order': 2592, 'label': '3C', 'order': 3, 'powers': [14, 1], 'representative': 190866170, 'size': 4}
    • id: 156458085
      {'aut_label': '3C', 'centralizer': '4.g1', 'counter': 15, 'group_counter': 65, 'group_order': 2592, 'label': '3D', 'order': 3, 'powers': [15, 1], 'representative': 191873739, 'size': 4}
    • id: 156458086
      {'aut_label': '3E', 'centralizer': '8.h1', 'counter': 16, 'group_counter': 65, 'group_order': 2592, 'label': '3E', 'order': 3, 'powers': [16, 1], 'representative': 2949152, 'size': 8}
    • id: 156458087
      {'aut_label': '3E', 'centralizer': '8.h1', 'counter': 17, 'group_counter': 65, 'group_order': 2592, 'label': '3F', 'order': 3, 'powers': [17, 1], 'representative': 191959344, 'size': 8}
    • id: 156458088
      {'aut_label': '3G', 'centralizer': '16.c1', 'counter': 18, 'group_counter': 65, 'group_order': 2592, 'label': '3G', 'order': 3, 'powers': [18, 1], 'representative': 17638795, 'size': 16}
    • id: 156458089
      {'aut_label': '3G', 'centralizer': '16.c1', 'counter': 19, 'group_counter': 65, 'group_order': 2592, 'label': '3H', 'order': 3, 'powers': [19, 1], 'representative': 17760402, 'size': 16}
    • id: 156458091
      {'aut_label': '3I', 'centralizer': '16.e1', 'counter': 20, 'group_counter': 65, 'group_order': 2592, 'label': '3I', 'order': 3, 'powers': [20, 1], 'representative': 1624912, 'size': 16}
    • id: 156458092
      {'aut_label': '4A', 'centralizer': '108.s1', 'counter': 21, 'group_counter': 65, 'group_order': 2592, 'label': '4A', 'order': 4, 'powers': [5, 21], 'representative': 382132008, 'size': 108}
    • id: 156458093
      {'aut_label': '4A', 'centralizer': '108.s1', 'counter': 22, 'group_counter': 65, 'group_order': 2592, 'label': '4B', 'order': 4, 'powers': [4, 22], 'representative': 394635241, 'size': 108}
    • id: 156458094
      {'aut_label': '4C', 'centralizer': '324.j1', 'counter': 23, 'group_counter': 65, 'group_order': 2592, 'label': '4C', 'order': 4, 'powers': [11, 23], 'representative': 360020599, 'size': 324}
    • id: 156458095
      {'aut_label': '6A', 'centralizer': '12.l1', 'counter': 24, 'group_counter': 65, 'group_order': 2592, 'label': '6A', 'order': 6, 'powers': [12, 2], 'representative': 7707779, 'size': 12}
    • id: 156458096
      {'aut_label': '6A', 'centralizer': '12.l1', 'counter': 25, 'group_counter': 65, 'group_order': 2592, 'label': '6B', 'order': 6, 'powers': [13, 3], 'representative': 7710607, 'size': 12}
    • id: 156458097
      {'aut_label': '6A', 'centralizer': '12.l1', 'counter': 26, 'group_counter': 65, 'group_order': 2592, 'label': '6C', 'order': 6, 'powers': [12, 2], 'representative': 94528435, 'size': 12}
    • id: 156458098
      {'aut_label': '6D', 'centralizer': '12.m1', 'counter': 27, 'group_counter': 65, 'group_order': 2592, 'label': '6D', 'order': 6, 'powers': [12, 3], 'representative': 94544515, 'size': 12}
    • id: 156458099
      {'aut_label': '6D', 'centralizer': '12.m1', 'counter': 28, 'group_counter': 65, 'group_order': 2592, 'label': '6E', 'order': 6, 'powers': [13, 2], 'representative': 94690363, 'size': 12}
    • id: 156458100
      {'aut_label': '6A', 'centralizer': '12.l1', 'counter': 29, 'group_counter': 65, 'group_order': 2592, 'label': '6F', 'order': 6, 'powers': [13, 3], 'representative': 94711596, 'size': 12}
    • id: 156458102
      {'aut_label': '6G', 'centralizer': '24.q1', 'counter': 30, 'group_counter': 65, 'group_order': 2592, 'label': '6G', 'order': 6, 'powers': [16, 2], 'representative': 8716114, 'size': 24}
    • id: 156458103
      {'aut_label': '6G', 'centralizer': '24.q1', 'counter': 31, 'group_counter': 65, 'group_order': 2592, 'label': '6H', 'order': 6, 'powers': [16, 3], 'representative': 8719198, 'size': 24}
    • id: 156458104
      {'aut_label': '6I', 'centralizer': '24.p1', 'counter': 32, 'group_counter': 65, 'group_order': 2592, 'label': '6I', 'order': 6, 'powers': [14, 2], 'representative': 95617196, 'size': 24}
    • id: 156458105
      {'aut_label': '6G', 'centralizer': '24.q1', 'counter': 33, 'group_counter': 65, 'group_order': 2592, 'label': '6J', 'order': 6, 'powers': [17, 3], 'representative': 95632669, 'size': 24}
    • id: 156458106
      {'aut_label': '6G', 'centralizer': '24.q1', 'counter': 34, 'group_counter': 65, 'group_order': 2592, 'label': '6K', 'order': 6, 'powers': [17, 2], 'representative': 95779268, 'size': 24}
    • id: 156458107
      {'aut_label': '6I', 'centralizer': '24.p1', 'counter': 35, 'group_counter': 65, 'group_order': 2592, 'label': '6L', 'order': 6, 'powers': [15, 3], 'representative': 95799631, 'size': 24}
    • id: 156458108
      {'aut_label': '6M', 'centralizer': '36.n1', 'counter': 36, 'group_counter': 65, 'group_order': 2592, 'label': '6M', 'order': 6, 'powers': [12, 6], 'representative': 15062989, 'size': 36}
    • id: 156458109
      {'aut_label': '6M', 'centralizer': '36.n1', 'counter': 37, 'group_counter': 65, 'group_order': 2592, 'label': '6N', 'order': 6, 'powers': [13, 6], 'representative': 15230070, 'size': 36}
    • id: 156458110
      {'aut_label': '6O', 'centralizer': '36.m1', 'counter': 38, 'group_counter': 65, 'group_order': 2592, 'label': '6O', 'order': 6, 'powers': [12, 4], 'representative': 87183545, 'size': 36}
    • id: 156458111
      {'aut_label': '6M', 'centralizer': '36.n1', 'counter': 39, 'group_counter': 65, 'group_order': 2592, 'label': '6P', 'order': 6, 'powers': [13, 7], 'representative': 87186378, 'size': 36}
    • id: 156458113
      {'aut_label': '6M', 'centralizer': '36.n1', 'counter': 40, 'group_counter': 65, 'group_order': 2592, 'label': '6Q', 'order': 6, 'powers': [12, 7], 'representative': 87204689, 'size': 36}
    • id: 156458114
      {'aut_label': '6O', 'centralizer': '36.m1', 'counter': 41, 'group_counter': 65, 'group_order': 2592, 'label': '6R', 'order': 6, 'powers': [13, 5], 'representative': 87206888, 'size': 36}
    • id: 156458115
      {'aut_label': '6S', 'centralizer': '36.c1', 'counter': 42, 'group_counter': 65, 'group_order': 2592, 'label': '6S', 'order': 6, 'powers': [15, 5], 'representative': 263497144, 'size': 36}
    • id: 156458116
      {'aut_label': '6S', 'centralizer': '36.c1', 'counter': 43, 'group_counter': 65, 'group_order': 2592, 'label': '6T', 'order': 6, 'powers': [14, 4], 'representative': 412890496, 'size': 36}
    • id: 156458117
      {'aut_label': '6U', 'centralizer': '48.a1', 'counter': 44, 'group_counter': 65, 'group_order': 2592, 'label': '6U', 'order': 6, 'powers': [18, 2], 'representative': 8842169, 'size': 48}
    • id: 156458118
      {'aut_label': '6U', 'centralizer': '48.a1', 'counter': 45, 'group_counter': 65, 'group_order': 2592, 'label': '6V', 'order': 6, 'powers': [19, 3], 'representative': 8845094, 'size': 48}
    • id: 156458119
      {'aut_label': '6W', 'centralizer': '72.o1', 'counter': 46, 'group_counter': 65, 'group_order': 2592, 'label': '6W', 'order': 6, 'powers': [16, 6], 'representative': 323539781, 'size': 72}
    • id: 156458120
      {'aut_label': '6X', 'centralizer': '72.bn1', 'counter': 47, 'group_counter': 65, 'group_order': 2592, 'label': '6X', 'order': 6, 'powers': [14, 8], 'representative': 217479894, 'size': 72}
    • id: 156458121
      {'aut_label': '6W', 'centralizer': '72.o1', 'counter': 48, 'group_counter': 65, 'group_order': 2592, 'label': '6Y', 'order': 6, 'powers': [17, 7], 'representative': 278375204, 'size': 72}
    • id: 156458122
      {'aut_label': '6X', 'centralizer': '72.bn1', 'counter': 49, 'group_counter': 65, 'group_order': 2592, 'label': '6Z', 'order': 6, 'powers': [15, 8], 'representative': 52796875, 'size': 72}
    • id: 156458124
      {'aut_label': '6AA', 'centralizer': '108.i1', 'counter': 50, 'group_counter': 65, 'group_order': 2592, 'label': '6AA', 'order': 6, 'powers': [12, 9], 'representative': 432157285, 'size': 108}
    • id: 156458125
      {'aut_label': '6AA', 'centralizer': '108.i1', 'counter': 51, 'group_counter': 65, 'group_order': 2592, 'label': '6AB', 'order': 6, 'powers': [13, 10], 'representative': 172130527, 'size': 108}
    • id: 156458126
      {'aut_label': '6AC', 'centralizer': '144.x1', 'counter': 52, 'group_counter': 65, 'group_order': 2592, 'label': '6AC', 'order': 6, 'powers': [20, 8], 'representative': 41742638, 'size': 144}
    • id: 156458127
      {'aut_label': '12A', 'centralizer': '216.bb1', 'counter': 53, 'group_counter': 65, 'group_order': 2592, 'label': '12A', 'order': 12, 'powers': [42, 21], 'representative': 281190952, 'size': 216}
    • id: 156458128
      {'aut_label': '12A', 'centralizer': '216.bb1', 'counter': 54, 'group_counter': 65, 'group_order': 2592, 'label': '12B', 'order': 12, 'powers': [43, 22], 'representative': 121160223, 'size': 216}
  • gps_qchar • Show schema
    • id: 15288692
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 15288703
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
    • id: 15288714
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}
    • id: 15288725
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
    • id: 15288736
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
    • id: 15288742
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
    • id: 15288743
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
    • id: 15288744
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1], 'schur_index': 1}
    • id: 15288745
      {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 2, -2, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'schur_index': 1}
    • id: 15288693
      {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, -2, -2, 2, 0, 0, 0, 2, 0, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, 0, -2, 0, 0, 2, 2, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288694
      {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 0, -2, -2, -2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288695
      {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 0, -2, -2, 2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288696
      {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 2, -2, 2, 0, 0, 0, -2, 0, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, -2, 0, 0, 2, 2, -2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288697
      {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
    • id: 15288698
      {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 4, -2, 4, 1, -2, -2, -2, 1, 1, 2, 0, 0, 0, -2, 0, 4, 0, -2, 0, -2, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 2, 0, -1, 0, 0, -1, -1, 0], 'schur_index': 1}
    • id: 15288699
      {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 2, 4, 0, 4, 2, 2, 0, 0, 2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, 2, 1, 2, 4, -1, 1, -1, 1, 2, 1, -1, -2, 2, -1, 0, -1, 2, 1, -2, 0, -1, -2, -1, 0, -1, 0, 0, -1, 0, 0, 0], 'schur_index': 1}
    • id: 15288700
      {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4c', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, -2, 4, 1, 4, -2, -2, 1, -2, 1, 0, 2, 0, -2, 0, -2, 0, 4, 0, -2, 0, 1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 2, 0, 0, -1, 0, -1], 'schur_index': 1}
    • id: 15288701
      {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4d', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 2, 4, 0, 2, 2, 0, 2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, 1, 2, 1, -1, 4, 2, 1, -1, -2, -1, 1, 2, -1, 2, 1, 2, -1, 0, 0, -2, -2, -1, -1, 0, -1, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288702
      {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4e', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, -2, 4, 0, 4, -2, -2, 0, 0, -2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, -2, 1, -2, 4, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, 0, 1, -2, 1, -2, 0, 1, -2, 1, 0, 1, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
    • id: 15288704
      {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4f', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, 4, 0, 4, 0, 0, -2, 0, 0, 0, 4, -2, 4, 1, -2, -2, -2, 1, 1, -2, 0, 0, 0, -2, 0, 4, 0, -2, 0, -2, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, -2, 0, 1, 0, 0, 1, 1, 0], 'schur_index': 1}
    • id: 15288705
      {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4g', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, -2, 4, 0, -2, -2, 0, -2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, 1, -2, 1, 1, 4, -2, 1, 1, -2, 1, 1, -2, 1, -2, 1, -2, 1, 0, 0, -2, -2, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288706
      {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4h', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 0, 0, 0, -2, 0, 0, 0, -2, 4, 1, 4, -2, -2, 1, -2, 1, 0, -2, 0, -2, 0, -2, 0, 4, 0, -2, 0, 1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, -2, 0, 0, 1, 0, 1], 'schur_index': 1}
    • id: 15288707
      {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4i', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, -2, 4, 0, 2, 2, 0, -2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, -1, -2, -1, 1, -4, -2, -1, 1, 2, 1, -1, -2, -1, 2, 1, 2, -1, 0, 0, -2, 2, 1, -1, 0, -1, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288708
      {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4j', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, 0, 4, 0, 0, 0, -2, 0, 0, 0, -2, 4, 1, 4, -2, -2, 1, -2, 1, 0, 2, 0, 2, 0, 2, 0, -4, 0, 2, 0, -1, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, -2, 0, 0, 1, 0, -1], 'schur_index': 1}
    • id: 15288709
      {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4k', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, 0, 4, 0, 0, 0, 2, 0, 0, 0, -2, 4, 1, 4, -2, -2, 1, -2, 1, 0, -2, 0, 2, 0, 2, 0, -4, 0, 2, 0, -1, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 2, 0, 0, -1, 0, 1], 'schur_index': 1}
    • id: 15288710
      {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4l', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -4, 2, 4, 0, -2, -2, 0, 2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, -1, 2, -1, -1, -4, 2, -1, -1, 2, -1, -1, 2, 1, -2, 1, -2, 1, 0, 0, -2, 2, -1, 1, 0, 1, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288711
      {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4m', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -2, -4, 0, 4, 2, 2, 0, 0, -2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, -2, -1, -2, -4, 1, -1, 1, -1, -2, -1, 1, 2, 2, -1, 0, -1, 2, 1, -2, 0, 1, 2, -1, 0, -1, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
    • id: 15288712
      {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4n', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 0, 0, -2, 0, 0, 0, 4, -2, 4, 1, -2, -2, -2, 1, 1, 2, 0, 0, 0, 2, 0, -4, 0, 2, 0, 2, 0, 2, 0, -1, 0, 0, 0, 0, 0, -2, 1, 0, 0, -1, 0, -2, 0, 1, 0, 0, 1, -1, 0], 'schur_index': 1}
    • id: 15288713
      {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4o', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 0, 0, 2, 0, 0, 0, 4, -2, 4, 1, -2, -2, -2, 1, 1, -2, 0, 0, 0, 2, 0, -4, 0, 2, 0, 2, 0, 2, 0, -1, 0, 0, 0, 0, 0, -2, 1, 0, 0, -1, 0, 2, 0, -1, 0, 0, -1, 1, 0], 'schur_index': 1}
    • id: 15288715
      {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4p', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, 2, -4, 0, 4, -2, -2, 0, 0, 2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, 2, -1, 2, -4, -1, -1, -1, -1, 2, -1, -1, 2, -2, 1, 0, 1, -2, 1, -2, 0, -1, 2, 1, 0, 1, 0, 0, -1, 0, 0, 0], 'schur_index': 1}
    • id: 15288716
      {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4q', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, -2, 0, 0, -4, -2, 2, 0, 0, 2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, -2, 3, -2, 0, 1, -3, 1, -3, -2, 3, 1, 0, -2, 1, 0, -1, 2, -1, 2, 0, 1, 0, 1, 0, -1, 0, 0, -1, 0, 0, 0], 'schur_index': 1}
    • id: 15288717
      {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4r', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, -2, 0, 0, -4, 2, -2, 0, 0, 2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, -2, -3, -2, 0, 1, 3, 1, 3, -2, -3, 1, 0, 2, -1, 0, 1, -2, -1, 2, 0, 1, 0, -1, 0, 1, 0, 0, -1, 0, 0, 0], 'schur_index': 1}
    • id: 15288718
      {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4s', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, 0, -2, -4, 0, -2, 2, 0, 2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, 3, -2, -3, 1, 0, -2, -3, 1, 0, 1, 3, -2, 1, -2, -1, 2, -1, 0, 0, 2, 0, 1, 1, 0, -1, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288719
      {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4t', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, 0, -2, -4, 0, 2, -2, 0, 2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, -3, -2, 3, 1, 0, -2, 3, 1, 0, 1, -3, -2, -1, 2, -1, -2, 1, 0, 0, 2, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288720
      {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4u', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, 0, 2, -4, 0, -2, 2, 0, -2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, -3, 2, 3, -1, 0, 2, 3, -1, 0, -1, -3, 2, 1, -2, -1, 2, -1, 0, 0, 2, 0, -1, 1, 0, -1, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288721
      {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4v', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, 0, 2, -4, 0, 2, -2, 0, -2, 0, 0, 1, 4, -2, 4, 1, 1, -2, 1, -2, 0, 0, 0, 3, 2, -3, -1, 0, 2, -3, -1, 0, -1, 3, 2, -1, 2, -1, -2, 1, 0, 0, 2, 0, -1, -1, 0, 1, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288722
      {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4w', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, 2, 0, 0, -4, -2, 2, 0, 0, -2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, 2, -3, 2, 0, -1, 3, -1, 3, 2, -3, -1, 0, -2, 1, 0, -1, 2, -1, 2, 0, -1, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
    • id: 15288723
      {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.4x', 'multiplicity': 1, 'nt': [12, 125], 'qdim': 4, 'qvalues': [4, 2, 0, 0, -4, 2, -2, 0, 0, -2, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, 2, 3, 2, 0, -1, -3, -1, -3, 2, 3, -1, 0, 2, -1, 0, 1, -2, -1, 2, 0, -1, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
    • id: 15288724
      {'cdim': 8, 'counter': 39, 'faithful': True, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.8a', 'multiplicity': 1, 'nt': [12, 248], 'qdim': 8, 'qvalues': [8, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, -4, -4, -4, 5, -1, -1, 2, 0, 0, 0, -2, -2, 4, -2, -2, 4, -2, -2, -2, 1, 1, -2, 0, 0, 0, -2, -2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288726
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    • id: 15288727
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    • id: 15288728
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    • id: 15288729
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    • id: 15288730
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    • id: 15288731
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    • id: 15288732
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    • id: 15288733
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    • id: 15288734
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    • id: 15288735
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    • id: 15288737
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    • id: 15288738
      {'cdim': 16, 'counter': 51, 'faithful': True, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.16c', 'multiplicity': 1, 'nt': [24, 5315], 'qdim': 16, 'qvalues': [16, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, 4, -8, -2, -2, 1, 4, -2, 0, 0, 0, -4, 0, -4, 0, -4, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288739
      {'cdim': 16, 'counter': 52, 'faithful': True, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.16d', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, 4, -8, -2, -2, 1, 4, -2, 0, 0, 0, 4, 0, 4, 0, 4, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288740
      {'cdim': 16, 'counter': 53, 'faithful': True, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.16e', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, -8, 4, -2, -2, 4, 1, -2, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15288741
      {'cdim': 16, 'counter': 54, 'faithful': True, 'group': '2592.cm', 'group_order': 2592, 'image': None, 'label': '2592.cm.16f', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -8, -8, 4, 4, 4, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, -1, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
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    • id: 35077507
      {'center': '4.b1', 'center_index': 4, 'center_order': 648, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1', 'kernel_order': 324, 'label': '2592.cm.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077508
      {'center': '4.b1', 'center_index': 4, 'center_order': 648, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1', 'kernel_order': 324, 'label': '2592.cm.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077509
      {'center': '4.a1', 'center_index': 4, 'center_order': 648, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 324, 'label': '2592.cm.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077510
      {'center': '4.a1', 'center_index': 4, 'center_order': 648, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 324, 'label': '2592.cm.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077511
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 15, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
    • id: 35077512
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 16, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[4, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077513
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 17, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4c', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
    • id: 35077514
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 18, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4d', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[4, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077515
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 19, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4e', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077517
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 20, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4f', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]]]}
    • id: 35077518
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4g', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077519
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 36, 'label': '2592.cm.4h', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
    • id: 35077520
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 18, 'label': '2592.cm.4i', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-4, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077521
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 18, 'label': '2592.cm.4j', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
    • id: 35077522
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 18, 'label': '2592.cm.4k', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
    • id: 35077523
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 18, 'label': '2592.cm.4l', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077524
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    • id: 35077525
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 28, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 18, 'label': '2592.cm.4n', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]]]}
    • id: 35077526
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 18, 'label': '2592.cm.4o', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]]]}
    • id: 35077528
      {'center': '72.a1', 'center_index': 72, 'center_order': 36, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 18, 'label': '2592.cm.4p', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077529
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4q', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077530
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4r', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077531
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 33, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4s', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077532
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 34, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4t', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077533
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4u', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077534
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4v', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[2, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077535
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4w', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077536
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.4x', 'nt': [12, 125], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077537
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8a', 'nt': [12, 248], 'q_character': None, 'values': [[[8, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077539
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8b', 'nt': [12, 248], 'q_character': None, 'values': [[[8, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077540
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 41, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.8c', 'nt': [24, 594], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[2, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077541
      {'center': '144.a1', 'center_index': 144, 'center_order': 18, 'counter': 42, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '288.889', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 9, 'label': '2592.cm.8d', 'nt': [24, 594], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077542
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8e', 'nt': [24, 5284], 'q_character': None, 'values': [[[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077543
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8f', 'nt': [24, 5284], 'q_character': None, 'values': [[[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077544
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 45, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8g', 'nt': [24, 5287], 'q_character': None, 'values': [[[8, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077545
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 46, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8h', 'nt': [24, 5287], 'q_character': None, 'values': [[[8, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077546
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 47, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8i', 'nt': [24, 5287], 'q_character': None, 'values': [[[8, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077547
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 48, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.8j', 'nt': [24, 5287], 'q_character': None, 'values': [[[8, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077548
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 49, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.16a', 'nt': [24, 5309], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077550
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 50, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.16b', 'nt': [24, 5315], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077551
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 51, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.16c', 'nt': [24, 5315], 'q_character': None, 'values': [[[16, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077552
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 52, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.16d', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077553
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 53, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.16e', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35077554
      {'center': '2592.a1', 'center_index': 2592, 'center_order': 1, 'counter': 54, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '2592.cm', 'group_counter': 65, 'group_order': 2592, 'image': None, 'image_isoclass': '2592.cm', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 1, 'label': '2592.cm.16f', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 438 matching records in this table.
    • id: 179423243
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '2592.cm.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.cm', 'subgroup_hash': 6952908971992144288, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 179423354
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3528', 'subgroup_hash': 3528, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 179423465
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423576
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3538', 'subgroup_hash': 3538, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 179423626
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3531', 'subgroup_hash': 3531, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:(C_2\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 179423637
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3497', 'subgroup_hash': 3497, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423648
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423659
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423670
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423244
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 179423255
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 179423266
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423277
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423288
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423299
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423310
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 179423321
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423332
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
    • id: 179423343
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423355
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423366
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423377
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423388
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423399
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423410
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423421
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423432
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423443
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423454
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423466
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423477
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423488
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423499
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423510
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 179423521
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423532
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423543
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423554
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423565
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423577
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
    • id: 179423588
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
    • id: 179423599
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423610
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423620
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423621
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423622
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423623
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423624
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423625
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
    • id: 179423627
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 179423628
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423629
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423630
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.12.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
    • id: 179423631
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 162, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
    • id: 179423632
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 162, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2592.cm.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 179423633
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 179423634
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
    • id: 179423635
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
    • id: 179423636
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 179423638
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 179423639
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423640
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
    • id: 179423641
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423642
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423643
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423644
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
    • id: 179423645
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423646
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 179423647
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 179423649
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 179423650
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423651
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423652
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423653
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423654
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423655
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423656
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423657
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423658
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423660
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423661
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423662
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423663
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
    • id: 179423664
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
    • id: 179423665
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423666
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423667
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423668
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423669
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423671
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423672
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423673
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423674
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423675
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423676
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423677
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423678
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 179423679
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 179423680
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 179423245
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2592.cm', 'ambient_counter': 65, 'ambient_order': 2592, 'ambient_tex': 'S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2592.cm.24.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 438 matching records in this table.
    • id: 179423243
      {'ambient': '2592.cm', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1', 'complements': ['2592.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8038, 3397, 7585, 3933], 'generators': [15214597, 167265, 263727360, 245419970, 166306490, 189626916, 1498112, 29606670, 131864130], 'label': '2592.cm.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.cm'}
    • id: 179423244
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '5184.gl', 'aut_weyl_index': 2, 'centralizer': '2592.a1', 'complements': ['648.b1', '648.e1', '648.k1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.e1'], 'contains': ['8.c1', '8.k1', '12.s1', '36.z1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [7840, 1969, 7914, 2443], 'generators': [121144894, 166306490, 189626916, 15214597, 167265, 263727360, 1498112], 'label': '2592.cm.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.b1', '2.e1'], 'normal_contains': ['8.c1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '2592.cm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '2592.cm'}
    • id: 179423245
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.h1', '12.r1', '12.s1'], 'contains': ['48.g1', '48.i1', '48.y1', '72.br1', '72.bt1', '72.by1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7463, -1, 7354, -1], 'generators': [1624912, 166306490, 189626916, 15214597, 263727360], 'label': '2592.cm.24.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bg1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 179423246
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.d1', '12.i1', '12.q1'], 'contains': ['48.h1', '48.j1', '48.ba1', '72.br1', '72.bs1', '72.by1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5023, -1, 5724, -1], 'generators': [166306490, 189626916, 15214597, 167265, 263727360], 'label': '2592.cm.24.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bh1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423247
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '216.162', 'aut_weyl_index': 48, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.l1', '12.b1', '12.c1', '12.e1'], 'contains': ['48.l1', '48.v2', '48.w1', '72.bz1', '72.ca1', '72.cb1', '72.cc1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3140, -1, 1468, -1], 'generators': [166306490, 435046886, 163699712, 15214597, 167265], 'label': '2592.cm.24.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bi1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423248
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.l1', '12.j1'], 'contains': ['48.m1', '48.u1', '72.ca1', '72.ch1'], 'core': '2592.a1', 'coset_action_label': '24T5286', 'count': 24, 'diagramx': [1113, -1, 538, -1], 'generators': [166306490, 435046886, 163699712, 14926470, 1498112], 'label': '2592.cm.24.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '24.bj1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423249
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '216.162', 'aut_weyl_index': 48, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.l1', '12.a1', '12.b1', '12.k1'], 'contains': ['48.n1', '48.v1', '48.v2', '72.cb1', '72.cc1', '72.ch1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2784, -1, 1760, -1], 'generators': [166306490, 435046886, 163699712, 15214597, 1498112], 'label': '2592.cm.24.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bk1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423250
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '12.j1'], 'contains': ['48.k1', '48.m1', '48.z1', '72.cd1', '72.cg1', '72.ci1'], 'core': '2592.a1', 'coset_action_label': '24T5284', 'count': 24, 'diagramx': [1925, -1, 357, -1], 'generators': [189626916, 15214597, 163720224, 29606670, 167265], 'label': '2592.cm.24.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '24.bl1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423251
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '216.162', 'aut_weyl_index': 48, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '12.e1', '12.k1', '12.q1'], 'contains': ['48.l1', '48.n1', '48.ba1', '72.cd1', '72.ce1', '72.cf1', '72.ci1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2006, -1, 850, -1], 'generators': [166306490, 189626916, 15214597, 29606670, 167265], 'label': '2592.cm.24.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bm1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423252
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '216.162', 'aut_weyl_index': 48, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.m1', '12.r1'], 'contains': ['48.o1', '48.q1', '48.y1', '72.cj1', '72.ck1', '72.cl1', '72.cn1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9235, -1, 9384, -1], 'generators': [1624912, 166306490, 189626916, 153882524, 15214597], 'label': '2592.cm.24.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '24.bn1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423253
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1'], 'contains': ['48.p1', '48.r1', '48.bb1', '72.ck1', '72.cm1', '72.cn1'], 'core': '2592.a1', 'coset_action_label': '24T5309', 'count': 24, 'diagramx': [9593, -1, 9062, -1], 'generators': [189626916, 153882524, 163720224, 167265, 16308666], 'label': '2592.cm.24.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bo1', 'old_label': '24.bo1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 179423254
      {'ambient': '2592.cm', 'aut_centralizer_order': 81, 'aut_label': '32.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '128.928', 'aut_weyl_index': 81, 'centralizer': '32.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.f1'], 'contains': ['96.a1', '96.b1', '96.c1', '96.d1', '96.e1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5900, 2959, 6412, 3560], 'generators': [166306490, 15214597, 167265, 1498112], 'label': '2592.cm.32.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1'], 'normal_contains': ['288.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '2592.cm', 'quotient_action_image': '32.27', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
    • id: 179423255
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '10368.bd', 'aut_weyl_index': 1, 'centralizer': '2592.a1', 'complements': ['648.b1', '648.k1', '648.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.c1', '8.n1', '36.bb1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [8829, 3990, 7291, 4550], 'generators': [166306490, 189626916, 139483822, 15214597, 167265, 263727360, 1498112], 'label': '2592.cm.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.c1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '2592.cm', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '2592.cm'}
    • id: 179423256
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.b1', '18.e1'], 'contains': ['72.c1', '72.g1', '72.h1', '72.bm1', '72.bq1', '72.cc1', '72.ch1', '108.a1', '108.b1'], 'core': '2592.a1', 'coset_action_label': '36T3916', 'count': 72, 'diagramx': [3257, -1, 2062, -1], 'generators': [412659706, 245419970, 15214597, 29606670, 164850290], 'label': '2592.cm.36.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.a1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423257
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '648.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.c1', '18.f1'], 'contains': ['72.d1', '72.f1', '72.bu1', '72.bw1', '72.cb1', '108.b1'], 'core': '144.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3811, -1, 3399, -1], 'generators': [412659706, 245419970, 15052669, 29606670, 164850290], 'label': '2592.cm.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.b1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423258
      {'ambient': '2592.cm', 'aut_centralizer_order': 6, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 216, 'centralizer': '432.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.g1', '18.a1'], 'contains': ['72.n1', '72.bi1', '72.bk1', '108.c1', '108.d1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8729, -1, 8823, -1], 'generators': [412659706, 166306490, 153882524, 15214597, 405440216], 'label': '2592.cm.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.c1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423259
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '648.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.a1', '18.b1', '18.f1'], 'contains': ['72.d1', '72.k1', '72.n1', '72.bj1', '72.by1', '108.e1', '108.f1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6630, -1, 6347, -1], 'generators': [166306490, 271347174, 189626916, 15214597, 263727360], 'label': '2592.cm.36.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.d1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423260
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '18.e1'], 'contains': ['72.h1', '72.l1', '72.o1', '72.bz1', '72.ci1', '108.g1', '108.h1'], 'core': '2592.a1', 'coset_action_label': '36T3914', 'count': 36, 'diagramx': [1966, -1, 961, -1], 'generators': [245419970, 189626916, 15214597, 29606670, 167265], 'label': '2592.cm.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.e1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423261
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 144, 'centralizer': '648.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '18.f1'], 'contains': ['72.p1', '72.u1', '72.bh1', '72.bj1', '72.cb1', '108.a1', '108.j1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5034, -1, 3300, -1], 'generators': [412659706, 245419970, 166306490, 15214597, 29606670], 'label': '2592.cm.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.f1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423262
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '18.e1'], 'contains': ['72.r1', '72.s1', '72.v1', '72.bl1', '72.bq1', '72.bz1', '72.cc1', '108.b1', '108.j1'], 'core': '2592.a1', 'coset_action_label': '36T3915', 'count': 72, 'diagramx': [3392, -1, 2160, -1], 'generators': [412659706, 245419970, 166306490, 15052669, 29606670], 'label': '2592.cm.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.g1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423263
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.h1'], 'contains': ['72.b1', '72.i1', '72.q1', '72.w1', '72.bb1', '72.bp1', '72.br1', '108.f1', '108.k1'], 'core': '2592.a1', 'coset_action_label': '36T3955', 'count': 72, 'diagramx': [6337, -1, 6673, -1], 'generators': [166428221, 271347174, 189626916, 15052669, 263727360], 'label': '2592.cm.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '36.h1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423264
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.i1', '18.e1'], 'contains': ['72.c1', '72.l1', '72.r1', '72.ba1', '72.bc1', '72.bq1', '72.bs1', '108.e1', '108.k1'], 'core': '2592.a1', 'coset_action_label': '36T3918', 'count': 72, 'diagramx': [4919, -1, 4136, -1], 'generators': [271347174, 189626916, 15214597, 164850290, 263727360], 'label': '2592.cm.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.i1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423265
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '12.j1'], 'contains': ['72.e1', '72.j1', '72.t1', '72.x1', '72.bd1', '72.ca1', '72.cd1', '108.h1', '108.l1'], 'core': '2592.a1', 'coset_action_label': '36T3971', 'count': 144, 'diagramx': [472, -1, 748, -1], 'generators': [245419970, 166306490, 189626916, 14926470, 29606670], 'label': '2592.cm.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '36.j1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423266
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2592.fs', 'aut_weyl_index': 4, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.b1', '8.e1', '8.f1', '8.i1', '8.l1', '12.a1', '12.b1', '12.c1'], 'core': '8.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3490, -1, 2800, -1], 'generators': [412659706, 245419970, 166306490, 15214597, 29606670, 167265, 1498112], 'label': '2592.cm.4.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.f1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
    • id: 179423267
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '648.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '12.k1', '18.f1'], 'contains': ['72.f1', '72.k1', '72.u1', '72.z1', '72.be1', '72.cb1', '72.ce1', '108.g1', '108.l1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1647, -1, 3202, -1], 'generators': [245419970, 166306490, 189626916, 15214597, 29606670], 'label': '2592.cm.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.k1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423268
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '12.k1', '18.e1'], 'contains': ['72.g1', '72.l1', '72.v1', '72.ba1', '72.bf1', '72.cc1', '72.cf1', '108.g1', '108.l1'], 'core': '2592.a1', 'coset_action_label': '36T3917', 'count': 72, 'diagramx': [1434, -1, 1668, -1], 'generators': [245419970, 189626916, 15214597, 29606670, 164850290], 'label': '2592.cm.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.l1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423269
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '216.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '18.f1'], 'contains': ['72.f1', '72.n1', '72.p1', '72.be1', '72.bh1', '108.i1', '108.m1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3958, -1, 3613, -1], 'generators': [412659706, 245419970, 166306490, 163699712, 15214597], 'label': '2592.cm.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '36.m1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423270
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '216.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.l1', '12.m1', '18.e1'], 'contains': ['72.c1', '72.g1', '72.o1', '72.s1', '72.bc1', '72.bf1', '72.bl1', '108.i1', '108.n1'], 'core': '2592.a1', 'coset_action_label': '36T3919', 'count': 72, 'diagramx': [2841, -1, 2592, -1], 'generators': [412659706, 245419970, 163699712, 15214597, 164850290], 'label': '2592.cm.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.n1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423271
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '432.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.g1', '18.c1'], 'contains': ['72.a1', '72.bv1', '72.bx1', '324.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8324, -1, 8493, -1], 'generators': [412659706, 153882524, 15052669, 164850290, 405440216], 'label': '2592.cm.36.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '36.o1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423272
      {'ambient': '2592.cm', 'aut_centralizer_order': 8, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '648.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.i1', '18.c1', '18.d1', '18.f1'], 'contains': ['72.a1', '72.p1', '72.z1', '72.bw1', '72.by1', '108.k1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7229, -1, 5306, -1], 'generators': [271347174, 189626916, 15052669, 164850290, 263727360], 'label': '2592.cm.36.p1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.p1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423273
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.k1', '18.e1'], 'contains': ['72.s1', '72.ba1', '72.bg1', '72.ch1', '72.ci1', '108.l1'], 'core': '2592.a1', 'coset_action_label': '36T3912', 'count': 36, 'diagramx': [1281, -1, 1366, -1], 'generators': [245419970, 166306490, 189626916, 29606670, 1498112], 'label': '2592.cm.36.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.q1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423274
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.l1', '12.n1', '18.e1'], 'contains': ['72.h1', '72.r1', '72.v1', '72.bc1', '72.bf1', '72.bg1', '72.bm1', '108.m1', '108.n1'], 'core': '2592.a1', 'coset_action_label': '36T3920', 'count': 24, 'diagramx': [2932, -1, 2906, -1], 'generators': [412659706, 245419970, 166306490, 163699712, 15052669], 'label': '2592.cm.36.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.r1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423275
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '216.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.m1', '12.n1', '18.f1'], 'contains': ['72.a1', '72.d1', '72.u1', '72.be1', '72.bu1', '108.n1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2712, -1, 3498, -1], 'generators': [412659706, 245419970, 163699712, 15052669, 164850290], 'label': '2592.cm.36.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.s1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423276
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 72, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.j1', '18.a1'], 'contains': ['72.bi1', '72.bj1', '72.bk1', '108.o1', '108.p1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8527, -1, 8601, -1], 'generators': [412659706, 166306490, 271347174, 153882524, 15214597], 'label': '2592.cm.36.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.t1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423277
      {'ambient': '2592.cm', 'aut_centralizer_order': 3, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4686', 'aut_weyl_index': 12, 'centralizer': '864.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.j1', '8.k1', '12.f1', '12.g1', '36.c1'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8334, -1, 8704, -1], 'generators': [412659706, 166306490, 153882524, 15214597, 167265, 405440216, 1498112], 'label': '2592.cm.4.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.g1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 179423278
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.q1', '18.e1'], 'contains': ['72.bl1', '72.bm1', '72.bs1', '72.cf1', '72.ci1', '108.q1'], 'core': '2592.a1', 'coset_action_label': '36T3913', 'count': 36, 'diagramx': [3545, -1, 1267, -1], 'generators': [189626916, 15214597, 29606670, 164850290, 263727360], 'label': '2592.cm.36.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.u1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423279
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '1296.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1'], 'contains': ['72.bn1', '72.bo1', '72.bt1', '72.cl1', '72.cn1', '108.r1'], 'core': '2592.a1', 'coset_action_label': '36T3962', 'count': 36, 'diagramx': [8991, -1, 9670, -1], 'generators': [189626916, 153882524, 163842099, 16060860, 263727360], 'label': '2592.cm.36.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.v1', 'old_label': '36.v1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423280
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '12.p1', '18.c1'], 'contains': ['72.bv1', '72.bw1', '72.bx1', '324.f1'], 'core': '144.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8173, -1, 8397, -1], 'generators': [412659706, 271347174, 153882524, 15052669, 164850290], 'label': '2592.cm.36.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.w1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423281
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '648.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.q1', '18.f1', '18.g1', '18.h1'], 'contains': ['72.bh1', '72.bu1', '72.by1', '72.ce1', '108.q1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6772, -1, 3729, -1], 'generators': [166306490, 189626916, 15214597, 29606670, 263727360], 'label': '2592.cm.36.x1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.x1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423282
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.r1', '18.a1', '18.c1', '18.g1'], 'contains': ['72.bi1', '72.bv1', '72.by1', '72.cj1', '108.r1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8828, -1, 8961, -1], 'generators': [166306490, 189626916, 153882524, 15214597, 263727360], 'label': '2592.cm.36.y1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.y1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 179423283
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '18.a1', '18.d1', '18.h1'], 'contains': ['72.bk1', '72.by1', '108.s1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8051, -1, 8018, -1], 'generators': [121144894, 166306490, 189626916, 15214597, 263727360], 'label': '2592.cm.36.z1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.z1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 179423284
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.s1', '18.b1', '18.c1', '18.h1'], 'contains': ['72.bx1', '72.by1', '324.i1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7936, -1, 7920, -1], 'generators': [121144894, 189626916, 15052669, 164850290, 263727360], 'label': '2592.cm.36.ba1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.ba1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 179423285
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '18.b1', '18.d1', '18.g1'], 'contains': ['72.by1', '72.co1', '324.j1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8412, -1, 7589, -1], 'generators': [166306490, 189626916, 139483822, 15214597, 263727360], 'label': '2592.cm.36.bb1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bb1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 179423286
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.k1', '18.g1'], 'contains': ['72.ce1', '72.cj1', '72.co1', '324.k1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9372, -1, 7478, -1], 'generators': [166306490, 189626916, 153882524, 15214597, 29606670], 'label': '2592.cm.36.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '36.bc1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423287
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.k1'], 'contains': ['72.cg1', '72.cm1', '72.cp1', '324.k1'], 'core': '2592.a1', 'coset_action_label': '36T4022', 'count': 72, 'diagramx': [9984, -1, 7253, -1], 'generators': [189626916, 153882524, 163720224, 29606670, 167265], 'label': '2592.cm.36.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bd1', 'old_label': '36.bd1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423288
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2592.cm', 'aut_weyl_index': 4, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.d1', '8.f1', '8.g1', '8.h1', '8.l1', '12.e1', '12.j1', '12.k1'], 'core': '8.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [2473, -1, 2187, -1], 'generators': [245419970, 166306490, 189626916, 15214597, 29606670, 167265, 1498112], 'label': '2592.cm.4.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.h1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
    • id: 179423289
      {'ambient': '2592.cm', 'aut_centralizer_order': 54, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 648, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '24.a1', '24.b1', '24.c1', '24.p1', '24.q1'], 'contains': ['96.d1', '144.b1', '144.c1', '144.d1', '144.e1', '144.f1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4380, -1, 4672, -1], 'generators': [166306490, 15214597, 167265, 405440216], 'label': '2592.cm.48.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.a1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 179423290
      {'ambient': '2592.cm', 'aut_centralizer_order': 27, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '24.k1'], 'contains': ['96.a1', '144.f1', '144.g1', '144.h1', '144.i1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5327, -1, 5366, -1], 'generators': [167265, 16308666, 164850290, 405440216], 'label': '2592.cm.48.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1', 'old_label': '48.b1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423291
      {'ambient': '2592.cm', 'aut_centralizer_order': 54, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '24.d1', '24.l1', '24.r1'], 'contains': ['96.b1', '144.b1', '144.g1', '144.i1', '144.j1'], 'core': '288.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6679, -1, 6337, -1], 'generators': [1624912, 16308666, 164850290, 405440216], 'label': '2592.cm.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '48.c1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423292
      {'ambient': '2592.cm', 'aut_centralizer_order': 27, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '24.g1', '24.m1', '24.t1'], 'contains': ['96.c1', '144.c1', '144.h1', '144.i1', '144.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [785, -1, 3764, -1], 'generators': [1624912, 15214597, 164850290, 405440216], 'label': '2592.cm.48.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.d1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423293
      {'ambient': '2592.cm', 'aut_centralizer_order': 54, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '48.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '24.e1', '24.h1', '24.j1', '24.n1', '24.q1', '24.s1', '24.u1'], 'contains': ['96.d1', '144.e1', '144.h1', '144.j1', '144.k1'], 'core': '288.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2317, -1, 3613, -1], 'generators': [15214597, 167265, 164850290, 405440216], 'label': '2592.cm.48.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.e1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423294
      {'ambient': '2592.cm', 'aut_centralizer_order': 54, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 216, 'centralizer': '48.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '24.f1', '24.i1', '24.o1', '24.p1', '24.u1'], 'contains': ['96.d1', '144.d1', '144.g1', '144.k1'], 'core': '288.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4219, -1, 4771, -1], 'generators': [166306490, 15214597, 405440216, 1498112], 'label': '2592.cm.48.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.f1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423295
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 216, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.d1', '24.w1', '24.bg1'], 'contains': ['96.b1', '144.l1', '144.m1', '144.p1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7515, -1, 7665, -1], 'generators': [1624912, 412659706, 166306490, 15214597], 'label': '2592.cm.48.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.g1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
    • id: 179423296
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 216, 'centralizer': '144.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.e1', '24.p1', '24.v1', '24.x1', '24.bh1'], 'contains': ['96.d1', '144.l1', '144.n1', '144.o1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5563, -1, 6028, -1], 'generators': [412659706, 166306490, 15214597, 167265], 'label': '2592.cm.48.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.h1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423297
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.r1', '24.ba1', '24.bb1', '24.bc1', '24.be1', '24.bf1', '24.bg1'], 'contains': ['96.b1', '144.a1', '144.n1', '144.p1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7652, -1, 7868, -1], 'generators': [1624912, 412659706, 16308666, 164850290], 'label': '2592.cm.48.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.i1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 179423298
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '144.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.a1', '24.f1', '24.s1', '24.y1', '24.z1', '24.bd1', '24.bh1'], 'contains': ['96.d1', '144.a1', '144.m1', '144.o1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4706, -1, 5821, -1], 'generators': [412659706, 15214597, 167265, 164850290], 'label': '2592.cm.48.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.j1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423299
      {'ambient': '2592.cm', 'aut_centralizer_order': 3, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4686', 'aut_weyl_index': 12, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.a1', '8.e1', '8.f1', '8.h1', '8.i1', '12.l1', '12.m1', '12.n1'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3204, -1, 2983, -1], 'generators': [412659706, 245419970, 166306490, 163699712, 15214597, 167265, 1498112], 'label': '2592.cm.4.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.i1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
    • id: 179423300
      {'ambient': '2592.cm', 'aut_centralizer_order': 9, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.38', 'aut_weyl_index': 216, 'centralizer': '288.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '24.g1', '24.bl1'], 'contains': ['96.c1', '144.q1', '144.r1', '144.v1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [939, -1, 44, -1], 'generators': [166306490, 14926470, 29606670, 1498112], 'label': '2592.cm.48.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.k1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423301
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '144.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '24.h1', '24.i1', '24.q1', '24.v1', '24.y1', '24.bi1', '24.bm1'], 'contains': ['96.d1', '144.q1', '144.s1', '144.t1', '144.u1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2202, -1, 1056, -1], 'generators': [166306490, 15214597, 29606670, 1498112], 'label': '2592.cm.48.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.l1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423302
      {'ambient': '2592.cm', 'aut_centralizer_order': 9, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '288.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '24.t1', '24.bj1', '24.bl1'], 'contains': ['96.c1', '144.s1', '144.v1', '144.w1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [706, -1, 197, -1], 'generators': [15214597, 163720224, 29606670, 167265], 'label': '2592.cm.48.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '48.m1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423303
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 144, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '24.b1', '24.j1', '24.u1', '24.v1', '24.z1', '24.bk1', '24.bm1'], 'contains': ['96.d1', '144.r1', '144.t1', '144.u1', '144.w1'], 'core': '288.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1819, -1, 954, -1], 'generators': [166306490, 15214597, 29606670, 167265], 'label': '2592.cm.48.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.n1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423304
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '24.w1', '24.ba1', '24.bn1'], 'contains': ['96.b1', '144.x1', '144.y1', '144.ba1', '144.bb1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9104, -1, 9663, -1], 'generators': [1624912, 166306490, 153882524, 15214597], 'label': '2592.cm.48.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '48.o1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423305
      {'ambient': '2592.cm', 'aut_centralizer_order': 9, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.38', 'aut_weyl_index': 216, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.bo1'], 'contains': ['96.e1', '144.x1', '144.z1', '144.bc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9593, -1, 9200, -1], 'generators': [153882524, 163720224, 167265, 16308666], 'label': '2592.cm.48.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bo1', 'old_label': '48.p1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423306
      {'ambient': '2592.cm', 'aut_centralizer_order': 18, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 144, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '24.w1', '24.bb1', '24.bn1'], 'contains': ['96.b1', '144.y1', '144.z1', '144.bb1', '144.bd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9183, -1, 9765, -1], 'generators': [1624912, 153882524, 16308666, 164850290], 'label': '2592.cm.48.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '48.q1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423307
      {'ambient': '2592.cm', 'aut_centralizer_order': 9, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '288.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.bo1'], 'contains': ['96.e1', '144.ba1', '144.bc1', '144.bd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9691, -1, 9302, -1], 'generators': [17760402, 153882524, 163720224, 167265], 'label': '2592.cm.48.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '48.r1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 179423308
      {'ambient': '2592.cm', 'aut_centralizer_order': 3, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 144, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '24.k1'], 'contains': ['96.a1', '144.be1', '144.bf1', '144.bg1', '144.bn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5406, -1, 5161, -1], 'generators': [271347174, 167265, 16308666, 164850290], 'label': '2592.cm.48.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '48.s1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 179423309
      {'ambient': '2592.cm', 'aut_centralizer_order': 6, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 144, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '24.d1', '24.l1', '24.bc1'], 'contains': ['96.b1', '144.be1', '144.bg1', '144.bh1', '144.bj1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6929, -1, 6130, -1], 'generators': [1624912, 271347174, 16308666, 164850290], 'label': '2592.cm.48.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1', 'old_label': '48.t1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423310
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2592.fs', 'aut_weyl_index': 4, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.j1', '8.k1', '12.o1', '12.p1', '36.t1'], 'core': '8.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8043, -1, 8397, -1], 'generators': [412659706, 166306490, 271347174, 153882524, 15214597, 167265, 1498112], 'label': '2592.cm.4.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.j1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '1296.3528'}
    • id: 179423311
      {'ambient': '2592.cm', 'aut_centralizer_order': 3, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 144, 'centralizer': '864.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '24.g1', '24.m1', '24.bj1'], 'contains': ['96.c1', '144.bf1', '144.bg1', '144.bi1', '144.bk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1094, -1, 3301, -1], 'generators': [1624912, 271347174, 15214597, 164850290], 'label': '2592.cm.48.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.u1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423312
      {'ambient': '2592.cm', 'aut_centralizer_order': 6, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.186', 'aut_weyl_index': 72, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '24.a1', '24.h1', '24.o1', '24.x1', '24.bk1'], 'contains': ['96.d1', '144.be1', '144.bi1', '144.bl1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4299, -1, 4471, -1], 'generators': [166306490, 271347174, 15214597, 1498112], 'label': '2592.cm.48.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.v1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423313
      {'ambient': '2592.cm', 'aut_centralizer_order': 6, 'aut_label': '48.v2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 144, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '24.b1', '24.e1', '24.i1', '24.n1', '24.bd1', '24.bi1', '24.bk1'], 'contains': ['96.d1', '144.bf1', '144.bh1', '144.bi1', '144.bm1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2983, -1, 3406, -1], 'generators': [271347174, 15214597, 167265, 164850290], 'label': '2592.cm.48.v2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.v2', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 179423314
      {'ambient': '2592.cm', 'aut_centralizer_order': 6, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '24.c1', '24.f1', '24.j1', '24.x1', '24.bi1'], 'contains': ['96.d1', '144.bj1', '144.bk1', '144.bl1', '144.bm1', '144.bn1'], 'core': '288.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4523, -1, 4382, -1], 'generators': [166306490, 271347174, 15214597, 167265], 'label': '2592.cm.48.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.w1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423315
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '216.162', 'aut_weyl_index': 48, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '24.k1'], 'contains': ['96.a1', '144.bo1', '144.bp1', '144.bq1', '144.bt1', '144.bu1', '144.bw1', '144.by1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5950, -1, 6956, -1], 'generators': [166306490, 189626916, 167265, 16308666], 'label': '2592.cm.48.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '48.x1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 179423316
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '24.l1', '24.bg1', '24.bn1'], 'contains': ['96.b1', '144.bo1', '144.bq1', '144.br1', '144.bu1', '144.bv1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7296, -1, 7437, -1], 'generators': [1624912, 166306490, 189626916, 15214597], 'label': '2592.cm.48.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.y1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 179423317
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '24.m1', '24.bl1'], 'contains': ['96.c1', '144.bp1', '144.bq1', '144.bs1', '144.bw1', '144.bx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3468, -1, 5556, -1], 'generators': [189626916, 15214597, 163720224, 167265], 'label': '2592.cm.48.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.z1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423318
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '24.c1', '24.n1', '24.o1', '24.bh1', '24.bm1'], 'contains': ['96.d1', '144.bo1', '144.bp1', '144.br1', '144.bs1', '144.bt1'], 'core': '288.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4617, -1, 5628, -1], 'generators': [166306490, 189626916, 15214597, 167265], 'label': '2592.cm.48.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ba1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 179423319
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.bo1'], 'contains': ['96.e1', '144.bt1', '144.bu1', '144.bv1', '144.bw1', '144.bx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8051, -1, 7580, -1], 'generators': [189626916, 163720224, 167265, 16308666], 'label': '2592.cm.48.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bo1', 'old_label': '48.bb1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 179423320
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 432, 'centralizer': '1296.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '18.a1'], 'contains': ['108.c1', '108.d1', '108.f1', '108.o1', '108.p1', '108.r1', '108.s1', '162.a1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8653, -1, 8704, -1], 'generators': [177442848, 271347174, 189626916, 153882524, 263727360], 'label': '2592.cm.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '54.a1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 179423321
      {'ambient': '2592.cm', 'aut_centralizer_order': 1, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2592.ci', 'aut_weyl_index': 4, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1'], 'contains': ['8.d1', '8.m1', '8.n1', '36.bc1', '36.bd1'], 'core': '8.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9375, -1, 7414, -1], 'generators': [166306490, 189626916, 153882524, 15214597, 29606670, 167265, 1498112], 'label': '2592.cm.4.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.k1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '1296.3531'}
    • id: 179423322
      {'ambient': '2592.cm', 'aut_centralizer_order': 8, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '324.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.e1', '18.f1'], 'contains': ['108.a1', '108.b1', '108.e1', '108.g1', '108.i1', '108.j1', '108.k1', '108.l1', '108.m1', '108.n1', '108.q1', '162.c1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4368, -1, 3103, -1], 'generators': [245419970, 166306490, 189626916, 29606670, 263727360], 'label': '2592.cm.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '54.b1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 179423323
      {'ambient': '2592.cm', 'aut_centralizer_order': 72, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '72.a1', 'complements': ['36.o1', '36.bc1', '36.bd1', '36.w1'], 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '24.s1', '36.o1', '36.p1', '36.s1'], 'contains': ['144.a1', '144.j1', '216.t1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7255, 7785, 5240, 8893], 'generators': [412659706, 15052669, 164850290, 405440216], 'label': '2592.cm.72.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '2592.cm', 'quotient_action_image': '72.40', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 179423324
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '432.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.d1', '36.h1'], 'contains': ['144.b1', '144.m1', '144.be1', '216.a1', '216.c1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6878, -1, 6532, -1], 'generators': [271347174, 16308666, 164850290, 263727360], 'label': '2592.cm.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '72.b1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423325
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '216.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.e1', '36.a1', '36.i1', '36.n1'], 'contains': ['144.e1', '144.o1', '144.bi1', '216.a1', '216.b1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3912, -1, 3907, -1], 'generators': [271347174, 15214597, 164850290, 263727360], 'label': '2592.cm.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.c1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423326
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '216.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.f1', '36.b1', '36.d1', '36.s1'], 'contains': ['144.a1', '144.d1', '144.bl1', '216.b1', '216.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5203, -1, 5926, -1], 'generators': [166306490, 271347174, 15214597, 263727360], 'label': '2592.cm.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.d1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423327
      {'ambient': '2592.cm', 'aut_centralizer_order': 6, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '432.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.g1', '36.j1'], 'contains': ['144.c1', '144.r1', '144.bf1', '216.d1', '216.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [72, -1, 756, -1], 'generators': [245419970, 14926470, 29606670, 164850290], 'label': '2592.cm.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '72.e1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423328
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '216.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.i1', '36.b1', '36.k1', '36.m1'], 'contains': ['144.d1', '144.t1', '144.bh1', '216.d1', '216.e1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2455, -1, 2734, -1], 'generators': [245419970, 15052669, 29606670, 164850290], 'label': '2592.cm.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.f1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423329
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '216.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.h1', '36.a1', '36.l1', '36.n1'], 'contains': ['144.e1', '144.u1', '144.bi1', '216.d1', '216.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1674, -1, 1765, -1], 'generators': [245419970, 15214597, 29606670, 164850290], 'label': '2592.cm.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.g1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423330
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '24.j1', '36.a1', '36.e1', '36.r1'], 'contains': ['144.e1', '144.w1', '144.bm1', '216.e1', '216.f1', '216.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1382, -1, 1210, -1], 'generators': [245419970, 15214597, 29606670, 167265], 'label': '2592.cm.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.h1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423331
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.l1', '36.h1'], 'contains': ['144.b1', '144.bj1', '144.bo1', '216.i1', '216.j1', '216.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6211, -1, 6235, -1], 'generators': [166428221, 271347174, 189626916, 15052669], 'label': '2592.cm.72.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '72.i1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423332
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '432.741', 'aut_weyl_index': 24, 'centralizer': '2592.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['12.f1', '12.g1', '12.h1', '12.o1', '12.p1', '12.r1', '12.s1', '18.c1', '54.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8207, -1, 8504, -1], 'generators': [1624912, 271347174, 189626916, 153882524, 16308666, 164850290, 263727360], 'label': '2592.cm.6.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '6.a1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 179423333
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.m1', '36.j1'], 'contains': ['144.c1', '144.bk1', '144.bp1', '216.h1', '216.k1', '216.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2302, -1, 4157, -1], 'generators': [166428221, 271347174, 189626916, 15214597], 'label': '2592.cm.72.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '72.j1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423334
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 144, 'centralizer': '648.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.o1', '36.d1', '36.k1'], 'contains': ['144.d1', '144.bl1', '144.br1', '216.h1', '216.j1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5102, -1, 5716, -1], 'generators': [166306490, 271347174, 189626916, 15214597], 'label': '2592.cm.72.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.k1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423335
      {'ambient': '2592.cm', 'aut_centralizer_order': 4, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '648.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.n1', '36.e1', '36.i1', '36.l1'], 'contains': ['144.e1', '144.bm1', '144.bs1', '216.h1', '216.i1', '216.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2657, -1, 3511, -1], 'generators': [166306490, 271347174, 189626916, 15052669], 'label': '2592.cm.72.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.l1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423336
      {'ambient': '2592.cm', 'aut_centralizer_order': 2, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.k1'], 'contains': ['144.f1', '144.bn1', '144.bt1', '216.j1', '216.k1', '216.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5536, -1, 5468, -1], 'generators': [166428221, 271347174, 189626916, 14926470], 'label': '2592.cm.72.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.m1', 'old_label': '72.m1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 179423337
      {'ambient': '2592.cm', 'aut_centralizer_order': 36, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 648, 'centralizer': '72.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '36.c1', '36.d1', '36.m1'], 'contains': ['144.d1', '144.l1', '216.m1', '216.n1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6630, -1, 6757, -1], 'generators': [412659706, 166306490, 15214597, 405440216], 'label': '2592.cm.72.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.n1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 179423338
      {'ambient': '2592.cm', 'aut_centralizer_order': 36, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1296, 'centralizer': '72.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1', '36.e1', '36.n1'], 'contains': ['144.e1', '144.q1', '216.o1', '216.p1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1598, -1, 1374, -1], 'generators': [245419970, 163699712, 15214597, 167265], 'label': '2592.cm.72.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.o1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 179423339
      {'ambient': '2592.cm', 'aut_centralizer_order': 24, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '216.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.e1', '36.f1', '36.m1', '36.p1'], 'contains': ['144.j1', '144.l1', '144.bh1', '216.a1', '216.q1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5312, -1, 4864, -1], 'generators': [271347174, 15052669, 164850290, 263727360], 'label': '2592.cm.72.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '72.p1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 179423340
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '432.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.f1', '36.h1'], 'contains': ['144.g1', '144.m1', '144.bj1', '216.c1', '216.q1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6431, -1, 6600, -1], 'generators': [166428221, 271347174, 15052669, 263727360], 'label': '2592.cm.72.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1', 'old_label': '72.q1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423341
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 288, 'centralizer': '216.u1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '24.f1', '36.g1', '36.i1', '36.r1'], 'contains': ['144.k1', '144.o1', '144.bm1', '216.b1', '216.q1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4002, -1, 3976, -1], 'generators': [166306490, 271347174, 15052669, 263727360], 'label': '2592.cm.72.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.r1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 179423342
      {'ambient': '2592.cm', 'aut_centralizer_order': 12, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 864, 'centralizer': '216.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.g1', '24.h1', '24.i1', '36.g1', '36.n1', '36.q1'], 'contains': ['144.k1', '144.q1', '144.bi1', '216.d1', '216.r1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1780, -1, 1580, -1], 'generators': [245419970, 166306490, 29606670, 1498112], 'label': '2592.cm.72.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.s1', 'projective_image': '2592.cm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}