-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5760.fv', 'ambient_counter': 152, 'ambient_order': 5760, 'ambient_tex': 'D_4\\times A_4\\times A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2880, 'characteristic': False, 'core_order': 4, 'counter': 1530, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5760.fv.1440.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1440.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1440.5850', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5850, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1440, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:\\GL(2,4)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '5760.fv', 'aut_centralizer_order': None, 'aut_label': '1440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': ['4.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['288.a1.b1', '480.b1.b1', '480.c1.b1', '480.d1.b1', '720.a1.a1', '720.c1.b1', '720.d1.b1', '720.e1.b1', '720.f1.b1', '720.g1.b1', '720.h1.b1'], 'contains': ['2880.a1.a1', '2880.b1.b1'], 'core': '1440.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6187, 8109, 7034, 9006, 7031, 5848, 6802, 6477], 'generators': [41040, 90720], 'label': '5760.fv.1440.a1.b1', 'mobius_quo': 0, 'mobius_sub': 240, 'normal_closure': '1440.a1.b1', 'normal_contained_in': ['24.a1.b1', '360.a1.b1', '720.a1.a1'], 'normal_contains': ['2880.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1440.a1.b1', 'projective_image': '2880.gn', 'quotient_action_image': '2.1', 'quotient_action_kernel': '720.768', 'quotient_action_kernel_order': 720, 'quotient_fusion': None, 'short_label': '1440.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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], [2, 1, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [2, 2, 2, 2, 6, 2, 4, 3, 2], 'aut_gens': [[43545600, 482630400, 482631120, 1037877840, 1037927520, 79924346, 958134971, 90720], [562464000, 482630400, 482631120, 1037877840, 1037968560, 1440765386, 1477012331, 131760], [562464000, 482630400, 482762160, 1037877840, 1037877120, 1440673946, 1476922331, 40320], [1476921600, 482630400, 482721120, 1037877840, 1037837520, 1001549546, 562504331, 720], [562464000, 482630400, 482670720, 1037877840, 1037968560, 1440765386, 1477012331, 131760], [958003200, 1520467200, 1520507520, 482671440, 482762160, 519050267, 1477012394, 131760], [43545600, 482630400, 482762160, 1037877840, 1037877120, 79873980, 958003939, 40320], [1001548800, 1520467200, 1520598960, 1037877840, 1037877120, 1476961946, 79834331, 40320], [1476921600, 1037836800, 1037837520, 1520508240, 1520557920, 1001639546, 43677371, 90720], [1476921600, 482630400, 482762160, 1037877840, 1037877120, 1001589146, 562464731, 40320]], 'aut_group': '23040.ch', 'aut_hash': 4448622648006636622, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 23040, 'aut_permdeg': 27, 'aut_perms': [403292434483114520192726550, 403292435701366285813284774, 2374509988355920784746087854, 403292436436216512260386854, 63382298663454176464646916, 6871124859217728413218325, 4747725386297074090774748208, 357405258060747636088216470, 2374509989334104553117813294], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 3, 1, 2], [2, 6, 2, 1], [2, 15, 1, 2], [2, 30, 2, 1], [2, 45, 1, 2], [2, 90, 2, 1], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 30, 1, 1], [4, 90, 1, 1], [5, 12, 2, 1], [6, 4, 2, 1], [6, 8, 4, 1], [6, 20, 1, 1], [6, 40, 2, 1], [6, 60, 1, 2], [6, 60, 2, 2], [6, 80, 2, 1], [6, 120, 2, 1], [6, 120, 4, 1], [6, 160, 4, 1], [10, 12, 2, 1], [10, 24, 4, 1], [10, 36, 2, 2], [10, 72, 4, 1], [12, 8, 2, 1], [12, 40, 1, 1], [12, 120, 1, 1], [12, 120, 2, 1], [12, 160, 2, 1], [15, 48, 4, 1], [20, 24, 2, 1], [20, 72, 2, 1], [30, 48, 4, 1], [30, 96, 8, 1], [60, 96, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_4\\times S_4\\times S_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '5760.co', 'autcentquo_hash': 6537139331229567448, 'autcentquo_nilpotent': False, 'autcentquo_order': 5760, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times S_4\\times S_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [2, 3, 2], [2, 6, 2], [2, 15, 2], [2, 30, 2], [2, 45, 2], [2, 90, 2], [3, 4, 2], [3, 20, 1], [3, 80, 2], [4, 2, 1], [4, 6, 1], [4, 30, 1], [4, 90, 1], [5, 12, 2], [6, 4, 2], [6, 8, 4], [6, 20, 1], [6, 40, 2], [6, 60, 6], [6, 80, 2], [6, 120, 6], [6, 160, 4], [10, 12, 2], [10, 24, 4], [10, 36, 4], [10, 72, 4], [12, 8, 2], [12, 40, 1], [12, 120, 3], [12, 160, 2], [15, 48, 4], [20, 24, 2], [20, 72, 2], [30, 48, 4], [30, 96, 8], [60, 96, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '2880.gn', 'commutator_count': 1, 'commutator_label': '480.1187', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '60.5'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 152, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['60.5', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 3, 1, 2], [2, 6, 1, 2], [2, 15, 1, 2], [2, 30, 1, 2], [2, 45, 1, 2], [2, 90, 1, 2], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 30, 1, 1], [4, 90, 1, 1], [5, 12, 2, 1], [6, 4, 2, 1], [6, 8, 2, 2], [6, 20, 1, 1], [6, 40, 1, 2], [6, 60, 1, 2], [6, 60, 2, 2], [6, 80, 2, 1], [6, 120, 1, 2], [6, 120, 2, 2], [6, 160, 2, 2], [10, 12, 2, 1], [10, 24, 2, 2], [10, 36, 2, 2], [10, 72, 2, 2], [12, 8, 2, 1], [12, 40, 1, 1], [12, 120, 1, 1], [12, 120, 2, 1], [12, 160, 2, 1], [15, 48, 4, 1], [20, 24, 2, 1], [20, 72, 2, 1], [30, 48, 4, 1], [30, 96, 4, 2], [60, 96, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 228, 'exponent': 60, 'exponents_of_order': [7, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[18, 1, 2], [24, 1, 1], [30, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2880.gn', 'hash': 5932148942766767589, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [3, 2, 2, 2, 2, 6, 6, 2], 'inner_gens': [[43545600, 1037836800, 1037837520, 1520508240, 1520557920, 79924346, 1477053371, 90720], [1476921600, 482630400, 482631120, 1037877840, 1037927520, 1001639546, 562595771, 90720], [1476921600, 482630400, 482631120, 1037877840, 1037968560, 1001680586, 562554731, 131760], [562464000, 482630400, 482631120, 1037877840, 1037927520, 1440724346, 1477053371, 90720], [562464000, 482630400, 482670720, 1037877840, 1037927520, 1440724346, 1477053371, 90720], [43545600, 1520467200, 1520507520, 482671440, 482721120, 79924346, 562595841, 90720], [562464000, 1037836800, 1037877120, 1520508240, 1520557920, 1440724375, 958134971, 90720], [43545600, 482630400, 482670720, 1037877840, 1037927520, 79924346, 958134971, 90720]], 'inner_hash': 5094570882729245637, 'inner_nilpotent': False, 'inner_order': 2880, 'inner_split': True, 'inner_tex': 'C_2^4:\\GL(2,4)', 'inner_used': [1, 2, 3, 5, 6, 7], 'irrC_degree': 18, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 18, 'irrep_stats': [[1, 12], [2, 3], [3, 28], [4, 12], [5, 12], [6, 7], [8, 3], [9, 8], [10, 3], [12, 4], [15, 4], [18, 2], [24, 1], [30, 1]], 'label': '5760.fv', 'linC_count': 288, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 16, 'linQ_dim': 9, 'linQ_dim_count': 16, 'linR_count': 32, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'D4*A4*A5', '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, 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': 48, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 100, 'number_divisions': 60, 'number_normal_subgroups': 36, 'number_subgroup_autclasses': 926, 'number_subgroup_classes': 1646, 'number_subgroups': 61958, 'old_label': None, 'order': 5760, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 383], [3, 188], [4, 128], [5, 24], [6, 2020], [10, 552], [12, 736], [15, 192], [20, 192], [30, 960], [60, 384]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [111, 0, 0], 'outer_gens': [[43545600, 482630400, 482631120, 1037877840, 1037927520, 79924375, 958135059, 90720], [43545600, 482630400, 482721120, 1037877840, 1037837520, 79834346, 958043531, 720], [79833600, 1037836800, 1037837520, 482671440, 482721120, 43636346, 519050171, 90720]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [3, 4], [4, 5], [5, 4], [6, 5], [8, 5], [10, 5], [12, 9], [15, 4], [16, 1], [18, 4], [20, 1], [24, 2], [30, 1], [36, 1]], 'representations': {'Perm': {'d': 13, 'gens': [43545600, 482630400, 482631120, 1037877840, 1037927520, 79924346, 958134971, 90720]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_4\\times A_4\\times A_5', 'transitive_degree': 60, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [12, 4], 'aut_gens': [[7378656, 10896487], [18879892, 4360336], [18879933, 4073147]], 'aut_group': '2880.dv', 'aut_hash': 409072078557532110, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2880, 'aut_permdeg': 26, 'aut_perms': [124326041322462899499688294, 149592909582738332237661751], 'aut_phi_ratio': 7.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 15, 1, 2], [2, 45, 1, 2], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [5, 12, 2, 1], [6, 4, 2, 1], [6, 20, 1, 1], [6, 60, 1, 2], [6, 60, 2, 2], [6, 80, 2, 1], [10, 12, 2, 1], [10, 36, 2, 2], [15, 48, 4, 1], [30, 48, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times S_5', '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': 60, 'autcentquo_group': '2880.dv', 'autcentquo_hash': 409072078557532110, 'autcentquo_nilpotent': False, 'autcentquo_order': 2880, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 15, 2], [2, 45, 2], [3, 4, 2], [3, 20, 1], [3, 80, 2], [5, 12, 2], [6, 4, 2], [6, 20, 1], [6, 60, 6], [6, 80, 2], [10, 12, 2], [10, 36, 4], [15, 48, 4], [30, 48, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '720.768', 'commutator_count': 1, 'commutator_label': '240.190', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '60.5'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 5850, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['2.1', 1], ['60.5', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 15, 1, 2], [2, 45, 1, 2], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [5, 12, 2, 1], [6, 4, 2, 1], [6, 20, 1, 1], [6, 60, 1, 2], [6, 60, 2, 2], [6, 80, 2, 1], [10, 12, 2, 1], [10, 36, 2, 2], [15, 48, 4, 1], [30, 48, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 228, 'exponent': 30, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[9, 1, 2], [12, 1, 1], [15, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1440.5850', 'hash': 5850, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [15, 6], 'inner_gens': [[7378656, 8397386], [12101845, 10896487]], 'inner_hash': 768, 'inner_nilpotent': False, 'inner_order': 720, 'inner_split': True, 'inner_tex': 'A_4\\times A_5', 'inner_used': [1, 2], 'irrC_degree': 9, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 9, 'irrep_stats': [[1, 6], [3, 14], [4, 6], [5, 6], [9, 4], [12, 2], [15, 2]], 'label': '1440.5850', 'linC_count': 18, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 3, 'linQ_dim': 7, 'linQ_dim_count': 3, 'linR_count': 6, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2^3:GL(2,4)', 'ngens': 2, '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, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 40, 'number_divisions': 24, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 180, 'number_subgroup_classes': 196, 'number_subgroups': 4334, 'old_label': None, 'order': 1440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 127], [3, 188], [5, 24], [6, 548], [10, 168], [15, 192], [30, 192]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [86, 0], 'outer_gens': [[7378650, 10896562], [4073136, 4360327]], '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': None, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [8, 2], [10, 2], [12, 4], [15, 2], [18, 2]], 'representations': {'Perm': {'d': 11, 'gens': [7378656, 10896487]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3:\\GL(2,4)', 'transitive_degree': 30, 'wreath_data': None, 'wreath_product': False}
