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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.30318', 'ambient_counter': 30318, 'ambient_order': 1728, 'ambient_tex': 'C_6^2:(C_4\\times D_6)', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 3, 'counter': 929, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.30318.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.8344', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8344, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4.S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.30318', 'aut_centralizer_order': 6912, 'aut_label': '576.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6912, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.c1.a1', '288.a1.a1', '288.b1.a1', '288.b1.b1', '288.i1.a1', '288.l1.a1', '288.l1.b1', '288.o1.a1', '288.s1.a1', '288.s1.b1', '288.s1.c1', '288.s1.d1'], 'contains': ['1728.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2506, 6119, 6372, 6907, 4477, 3900, 3738, 6670], 'generators': [576], 'label': '1728.30318.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['144.b1.a1', '192.a1.a1', '288.b1.a1', '288.b1.b1', '288.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '1728.30318', 'quotient_action_image': '2.1', 'quotient_action_kernel': '288.916', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [2]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [3, 1, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3.1', 'hash': 1, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 3]], 'label': '3.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 3, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 3, 'order_factorization_type': 1, 'order_stats': [[1, 1], [3, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 3, 'pgroup': 3, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -3]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [7]}, 'Lie': [{'d': 1, 'q': 3, 'gens': [3], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [7]}, 'Perm': {'d': 3, 'gens': [4]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [3], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3', 'transitive_degree': 3, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 6, 6, 2, 6], 'aut_gens': [[1, 2, 24, 144, 288], [729, 1514, 384, 144, 360], [873, 1694, 1488, 144, 1512], [297, 1226, 1488, 156, 1512], [1449, 1450, 1488, 144, 1224], [733, 1202, 120, 144, 1440], [157, 1502, 24, 144, 288]], 'aut_group': None, 'aut_hash': 8171187662760836131, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 13824, 'aut_permdeg': 108, 'aut_perms': [752923914603659140369413512394553635679513164189438720379016000739327119088186336369173411739819760455651149731701596107826036950712498143016069229376260810990899551443219953, 1023738537998225683751634904482283475497412806616289789138051662809056748465122017122751702318430545236140227518468656655793664641514402169536855711460794970800727009347895370, 1157040309211349421516455708493418380991486712764855487065388344170152163099731106659130035924512654447301915471047105021498561186324921955694332391831004511006914991728305493, 1153091035772859710206349586405258095202194939962948475479569211485440673626793189746176467630155253293281926246095770196281544078281778454050050251933193162525384193195504002, 238460193862469531903439977246269065592524392470147101344045208010626039125068701018174476760396493220555115014233889327374287861485703771575598187626265019841369417420427790, 717367228548935126452162086243498288168338797902889922897398044810786705951586288246638229355599665454970259692127379677543458867886015542864380679697338916172620817007999496], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 18, 4, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 9, 4, 1], [4, 18, 4, 3], [4, 27, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 1, 5], [6, 6, 2, 3], [6, 12, 1, 2], [6, 12, 2, 1], [6, 24, 1, 1], [6, 24, 2, 1], [6, 36, 4, 1], [6, 48, 1, 1], [6, 48, 2, 1], [12, 36, 4, 3], [12, 72, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2:C_3.C_2^5.C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 18, 4], [3, 2, 1], [3, 6, 1], [3, 24, 1], [3, 48, 1], [4, 9, 4], [4, 18, 12], [4, 27, 4], [6, 2, 3], [6, 6, 11], [6, 12, 4], [6, 24, 3], [6, 36, 4], [6, 48, 3], [12, 36, 12], [12, 72, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '432.523', 'commutator_count': 1, 'commutator_label': '108.22', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 30318, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['864.2237', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 18, 1, 4], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 9, 2, 2], [4, 18, 1, 4], [4, 18, 2, 4], [4, 27, 2, 2], [6, 2, 1, 3], [6, 6, 1, 11], [6, 12, 1, 4], [6, 24, 1, 3], [6, 36, 1, 4], [6, 48, 1, 3], [12, 36, 1, 4], [12, 36, 2, 4], [12, 72, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 90720, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '288.1028', 'hash': 30318, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 6, 1, 6], 'inner_gens': [[1, 10, 24, 144, 1512], [17, 2, 408, 144, 648], [1, 1490, 24, 144, 288], [1, 2, 24, 144, 288], [649, 1514, 24, 144, 288]], 'inner_hash': 523, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'C_6^2:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 16], [3, 16], [4, 4], [6, 24], [12, 4]], 'label': '1728.30318', 'linC_count': 48, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 16, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:(C4*D6)', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 38, 'number_characteristic_subgroups': 31, 'number_conjugacy_classes': 80, 'number_divisions': 66, 'number_normal_subgroups': 79, 'number_subgroup_autclasses': 474, 'number_subgroup_classes': 944, 'number_subgroups': 8635, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 87], [3, 80], [4, 360], [6, 480], [12, 720]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[157, 22, 120, 144, 360], [145, 146, 120, 144, 1440], [13, 10, 24, 144, 1512], [145, 146, 120, 156, 1440]], 'outer_group': '32.27', 'outer_hash': 27, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [55, 107, 5329, 40212], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [3, 8], [4, 6], [6, 20], [12, 8]], 'representations': {'PC': {'code': 8838734340292395897617292927692221319801894801691199393294637775246834215977, 'gens': [1, 2, 5, 7, 8], 'pres': [9, 2, 2, 2, 3, 2, 3, 2, 2, 3, 181, 46, 542, 74, 579, 9193, 4342, 8266, 130, 18158, 8447, 8132, 108871, 23344, 6505, 11050, 214, 93320, 46673]}, 'Perm': {'d': 19, 'gens': [93884316655, 732297649721850, 3628800, 186810624000, 376610218036676, 16371, 104197, 6423296495616000, 13516122267648000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:(C_4\\times D_6)', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [3, 2, 12, 2, 12, 6, 4, 6, 3, 2, 2], 'aut_gens': [[88011, 8111, 110352, 12201, 91483], [88011, 90001, 110352, 88211, 95283], [88011, 8111, 110352, 12201, 28931], [152019, 88101, 76466, 12201, 91483], [88011, 88101, 26342, 12201, 91483], [88011, 8311, 112661, 92011, 91483], [88011, 134316, 11744, 92011, 15493], [88011, 38304, 135949, 88211, 104921], [152019, 10011, 156466, 88211, 25131], [88011, 8111, 111712, 12201, 91483], [88011, 8111, 66157, 92011, 91483], [88011, 88101, 106152, 12201, 91483]], 'aut_group': '4608.lt', 'aut_hash': 7796095685647803946, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 36, 'aut_perms': [255609202217806398574120340612846547895929, 4737510039594141439661171762220, 23032989978124022513048170913159585404960, 209403106561538948738297601305063237745513, 263796456529173581610465676441847406293741, 324890944742956669014333240195415604509284, 295728021972614229542051662938375734669700, 152085797044042481716340515150664500937320, 552926751738406423943877092402340, 284162383959880718701596295786400019214089, 4901360659526995270963915348053895800], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 6, 4, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 3, 4, 1], [4, 6, 4, 1], [4, 9, 4, 1], [4, 18, 4, 2], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 1, 2], [6, 6, 2, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 12, 4, 1], [6, 16, 1, 1], [6, 16, 2, 1], [12, 12, 4, 1], [12, 24, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5.D_6^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '144.183', 'autcentquo_hash': 183, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 6, 4], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 3, 4], [4, 6, 4], [4, 9, 4], [4, 18, 8], [6, 2, 3], [6, 6, 4], [6, 8, 3], [6, 12, 4], [6, 16, 3], [12, 12, 4], [12, 24, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '144.183', 'commutator_count': 1, 'commutator_label': '36.11', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8344, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['12.1', 1], ['2.1', 1], ['24.12', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 6, 1, 4], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 3, 2, 2], [4, 6, 1, 4], [4, 9, 2, 2], [4, 18, 2, 4], [6, 2, 1, 3], [6, 6, 1, 4], [6, 8, 1, 3], [6, 12, 1, 4], [6, 16, 1, 3], [12, 12, 1, 4], [12, 24, 2, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 10080, 'exponent': 12, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '288.1028', 'hash': 8344, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [1, 2, 6, 2, 6], 'inner_gens': [[88011, 8111, 110352, 12201, 91483], [88011, 8111, 66157, 92011, 91483], [88011, 134316, 110352, 92011, 104921], [88011, 88101, 106152, 12201, 91483], [88011, 8111, 156466, 12201, 91483]], 'inner_hash': 183, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'S_3\\times S_4', 'inner_used': [2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 16], [3, 16], [4, 4], [6, 8]], 'label': '576.8344', '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': True, 'name': 'C2^4.S3^2', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 60, 'number_divisions': 50, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 240, 'number_subgroup_classes': 482, 'number_subgroups': 2364, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 39], [3, 26], [4, 216], [6, 150], [12, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [8001, 8001, 8001, 8001], 'outer_gens': [[88011, 152309, 98073, 92011, 28931], [88011, 88301, 102263, 92011, 28931], [88011, 72119, 110352, 12201, 28931], [152019, 88301, 58068, 12201, 28931]], 'outer_group': '32.27', 'outer_hash': 27, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [2306, 3758, 12341, 30801], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [3, 8], [4, 6], [6, 12]], 'representations': {'PC': {'code': 67621433625216537174708338970121321240345503091721, 'gens': [1, 2, 3, 6, 7], 'pres': [8, -2, -2, -2, -2, -3, -2, 2, -3, 250, 66, 651, 91, 652, 8077, 4053, 1757, 1045, 3382, 1038, 1550, 166, 6167]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [92011, 11293, 12201, 72009, 130106, 130311, 24247, 8201]}, 'Perm': {'d': 13, 'gens': [522587640, 1037836802, 40320, 1037836800, 3, 840, 7, 16]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4.S_3^2', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
