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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.322278', 'ambient_counter': 322278, 'ambient_order': 768, 'ambient_tex': '(D_6\\times C_2^4):C_4', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 1, 'counter': 444, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '768.322278.768.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '768.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '768.322278', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 322278, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(D_6\\times C_2^4):C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'D2', 'C9'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
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{'ambient': '768.322278', 'aut_centralizer_order': None, 'aut_label': '768.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['256.a1', '384.a1', '384.b1', '384.c1', '384.d1', '384.e1', '384.f1', '384.g1', '384.h1', '384.i1'], 'contains': [], 'core': '768.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '768.322278.768.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '768.a1', 'normal_contained_in': ['256.a1', '384.a1', '384.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '768.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, '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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [12, 4, 2, 4, 12, 4], 'aut_gens': [[94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [381807861143, 281174706847, 282132668183, 7, 1960277760, 211890026880, 269681892480, 282132668160, 840], [120831822736, 269682256943, 282132668183, 282132668176, 20677265280, 555732938880, 19200746880, 282132668160, 1440], [610372183687, 766216, 282132668167, 16, 1960277760, 211890026880, 19200746880, 282132668160, 840], [437496111376, 1959915016, 282132668183, 16, 20677265280, 555732938880, 269681892480, 282132668160, 840], [120353184007, 282132306847, 23, 16, 268241662080, 561960322560, 19200746880, 282132668160, 840], [437496111367, 268240896143, 7, 282132668176, 268241662080, 555732938880, 269681892480, 282132668160, 840]], 'aut_group': None, 'aut_hash': 8292658654992033635, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 294912, 'aut_permdeg': 160, 'aut_perms': [275529822447691959153552011845283964851731727775551817039261991299654389769947703658109633704937303587978920692313040560317038111402380182080623814627244550707814680500101942670626496573521390839298984086377385290726332780362404999755783871232994196756278106503747335279769641790548999, 377146780390204610996846158480418163807741412994695143525030514375618504509364632014722290824340616240960676336371502741536784251495473649467386598899639460687347279902975952443522944792087385261897897285096206407477459414152186744631020011010329752239976094450380419187024118414229078, 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126303984917821637797561500924917156952500040543506003232977594961372671934530438198856963538196812872389212476391185693926162914294127605718171093530920606671760327771807641417497312805854046198951995034497725678549404140408682496089333938193166855349703802896173131071395081710346101], 'aut_phi_ratio': 1152.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 2, 1, 1], [2, 2, 3, 1], [2, 4, 1, 2], [2, 4, 3, 2], [2, 12, 8, 1], [3, 2, 1, 1], [4, 4, 1, 1], [4, 4, 3, 1], [4, 8, 8, 1], [4, 24, 4, 1], [6, 2, 1, 1], [6, 2, 6, 1], [6, 4, 1, 1], [6, 4, 2, 1], [6, 4, 3, 1], [6, 4, 6, 1], [6, 8, 1, 1], [6, 8, 3, 1], [8, 24, 8, 1], [12, 8, 1, 1], [12, 8, 3, 1], [12, 8, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.C_2^4.D_6^2.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': None, 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4.C_2^4.S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': None, 'autcentquo_hash': 1147, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times C_2^2\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [2, 4, 8], [2, 12, 8], [3, 2, 1], [4, 4, 4], [4, 8, 8], [4, 24, 4], [6, 2, 7], [6, 4, 12], [6, 8, 4], [8, 24, 8], [12, 8, 20]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '96.13', 'commutator_count': 1, 'commutator_label': '24.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 322278, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['192.30', 1], ['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [2, 4, 1, 8], [2, 12, 1, 8], [3, 2, 1, 1], [4, 4, 1, 4], [4, 8, 2, 4], [4, 24, 1, 4], [6, 2, 1, 7], [6, 4, 1, 4], [6, 4, 2, 4], [6, 8, 1, 4], [8, 24, 2, 4], [12, 8, 1, 4], [12, 8, 4, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 349440, 'exponent': 24, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.11', 'frattini_quotient': '48.51', 'hash': 322278, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 2, 1, 1, 2, 2, 2, 1, 3], 'inner_gens': [[94929448320, 1959915000, 7, 16, 1960277760, 199395302400, 269681892480, 282132668160, 840], [381807861120, 19199980920, 7, 16, 20677265280, 211890026880, 19200746880, 282132668160, 1440], [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [363613057920, 19199980920, 7, 16, 20677265280, 561960322560, 19200746880, 282132668160, 840], [94929448320, 766200, 7, 16, 268241662080, 199395302400, 19200746880, 282132668160, 840], [382287225600, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [94929448320, 19199982360, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': False, 'inner_tex': 'C_2^2.D_{12}', 'inner_used': [1, 2, 9], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 40], [4, 20], [8, 4]], 'label': '768.322278', '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': True, 'metacyclic': False, 'monomial': True, 'name': '(D6*C2^4):C4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 33, 'number_conjugacy_classes': 96, 'number_divisions': 72, 'number_normal_subgroups': 291, 'number_subgroup_autclasses': 444, 'number_subgroup_classes': 2774, 'number_subgroups': 15652, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 143], [3, 2], [4, 176], [6, 94], [8, 192], [12, 160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 6, 4, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[630486581767, 269682255487, 282132668183, 282132668167, 281173939200, 199395302400, 19200746880, 282132668160, 1440], [436054752016, 269682255480, 282132668183, 282132668167, 281173939200, 199395302400, 19200746880, 282132668160, 840], [436054752000, 269682255503, 16, 282132668167, 281173939200, 199395302400, 19200746880, 282132668160, 840], [94929448343, 19199980920, 23, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840]], 'outer_group': None, 'outer_hash': 388097117244947847, 'outer_nilpotent': False, 'outer_order': 3072, 'outer_permdeg': 16, 'outer_perms': [2896083597023, 1332706194136, 8383613384280, 1340370235456], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2.C_2^6.C_6.C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 24], [8, 8]], 'representations': {'PC': {'code': '12519182639920090126574719018471989318343250243496456', 'gens': [1, 3, 5, 7, 8, 9], 'pres': [9, 2, 2, 2, 2, 2, 3, 2, 2, 2, 18, 1406, 173, 74, 15843, 1084, 10093, 4702, 130, 887, 31760, 1961, 998]}, 'Perm': {'d': 15, 'gens': [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(D_6\\times C_2^4):C_4', 'transitive_degree': 96, '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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [12, 4, 2, 4, 12, 4], 'aut_gens': [[94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [381807861143, 281174706847, 282132668183, 7, 1960277760, 211890026880, 269681892480, 282132668160, 840], [120831822736, 269682256943, 282132668183, 282132668176, 20677265280, 555732938880, 19200746880, 282132668160, 1440], [610372183687, 766216, 282132668167, 16, 1960277760, 211890026880, 19200746880, 282132668160, 840], [437496111376, 1959915016, 282132668183, 16, 20677265280, 555732938880, 269681892480, 282132668160, 840], [120353184007, 282132306847, 23, 16, 268241662080, 561960322560, 19200746880, 282132668160, 840], [437496111367, 268240896143, 7, 282132668176, 268241662080, 555732938880, 269681892480, 282132668160, 840]], 'aut_group': None, 'aut_hash': 8292658654992033635, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 294912, 'aut_permdeg': 160, 'aut_perms': [275529822447691959153552011845283964851731727775551817039261991299654389769947703658109633704937303587978920692313040560317038111402380182080623814627244550707814680500101942670626496573521390839298984086377385290726332780362404999755783871232994196756278106503747335279769641790548999, 377146780390204610996846158480418163807741412994695143525030514375618504509364632014722290824340616240960676336371502741536784251495473649467386598899639460687347279902975952443522944792087385261897897285096206407477459414152186744631020011010329752239976094450380419187024118414229078, 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126303984917821637797561500924917156952500040543506003232977594961372671934530438198856963538196812872389212476391185693926162914294127605718171093530920606671760327771807641417497312805854046198951995034497725678549404140408682496089333938193166855349703802896173131071395081710346101], 'aut_phi_ratio': 1152.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 2, 1, 1], [2, 2, 3, 1], [2, 4, 1, 2], [2, 4, 3, 2], [2, 12, 8, 1], [3, 2, 1, 1], [4, 4, 1, 1], [4, 4, 3, 1], [4, 8, 8, 1], [4, 24, 4, 1], [6, 2, 1, 1], [6, 2, 6, 1], [6, 4, 1, 1], [6, 4, 2, 1], [6, 4, 3, 1], [6, 4, 6, 1], [6, 8, 1, 1], [6, 8, 3, 1], [8, 24, 8, 1], [12, 8, 1, 1], [12, 8, 3, 1], [12, 8, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.C_2^4.D_6^2.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': None, 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4.C_2^4.S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': None, 'autcentquo_hash': 1147, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times C_2^2\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [2, 4, 8], [2, 12, 8], [3, 2, 1], [4, 4, 4], [4, 8, 8], [4, 24, 4], [6, 2, 7], [6, 4, 12], [6, 8, 4], [8, 24, 8], [12, 8, 20]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '96.13', 'commutator_count': 1, 'commutator_label': '24.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 322278, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['192.30', 1], ['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [2, 4, 1, 8], [2, 12, 1, 8], [3, 2, 1, 1], [4, 4, 1, 4], [4, 8, 2, 4], [4, 24, 1, 4], [6, 2, 1, 7], [6, 4, 1, 4], [6, 4, 2, 4], [6, 8, 1, 4], [8, 24, 2, 4], [12, 8, 1, 4], [12, 8, 4, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 349440, 'exponent': 24, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.11', 'frattini_quotient': '48.51', 'hash': 322278, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 2, 1, 1, 2, 2, 2, 1, 3], 'inner_gens': [[94929448320, 1959915000, 7, 16, 1960277760, 199395302400, 269681892480, 282132668160, 840], [381807861120, 19199980920, 7, 16, 20677265280, 211890026880, 19200746880, 282132668160, 1440], [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [363613057920, 19199980920, 7, 16, 20677265280, 561960322560, 19200746880, 282132668160, 840], [94929448320, 766200, 7, 16, 268241662080, 199395302400, 19200746880, 282132668160, 840], [382287225600, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840], [94929448320, 19199982360, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': False, 'inner_tex': 'C_2^2.D_{12}', 'inner_used': [1, 2, 9], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 40], [4, 20], [8, 4]], 'label': '768.322278', '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': True, 'metacyclic': False, 'monomial': True, 'name': '(D6*C2^4):C4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 33, 'number_conjugacy_classes': 96, 'number_divisions': 72, 'number_normal_subgroups': 291, 'number_subgroup_autclasses': 444, 'number_subgroup_classes': 2774, 'number_subgroups': 15652, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 143], [3, 2], [4, 176], [6, 94], [8, 192], [12, 160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 6, 4, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[630486581767, 269682255487, 282132668183, 282132668167, 281173939200, 199395302400, 19200746880, 282132668160, 1440], [436054752016, 269682255480, 282132668183, 282132668167, 281173939200, 199395302400, 19200746880, 282132668160, 840], [436054752000, 269682255503, 16, 282132668167, 281173939200, 199395302400, 19200746880, 282132668160, 840], [94929448343, 19199980920, 23, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840]], 'outer_group': None, 'outer_hash': 388097117244947847, 'outer_nilpotent': False, 'outer_order': 3072, 'outer_permdeg': 16, 'outer_perms': [2896083597023, 1332706194136, 8383613384280, 1340370235456], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2.C_2^6.C_6.C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 24], [8, 8]], 'representations': {'PC': {'code': '12519182639920090126574719018471989318343250243496456', 'gens': [1, 3, 5, 7, 8, 9], 'pres': [9, 2, 2, 2, 2, 2, 3, 2, 2, 2, 18, 1406, 173, 74, 15843, 1084, 10093, 4702, 130, 887, 31760, 1961, 998]}, 'Perm': {'d': 15, 'gens': [94929448320, 19199980920, 7, 16, 20677265280, 199395302400, 19200746880, 282132668160, 840]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(D_6\\times C_2^4):C_4', 'transitive_degree': 96, 'wreath_data': None, 'wreath_product': False}
