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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1536.1699', 'ambient_counter': 1699, 'ambient_order': 1536, 'ambient_tex': 'C_8\\times C_{192}', 'central': True, 'central_factor': False, 'centralizer_order': 1536, 'characteristic': True, 'core_order': 4, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1536.1699.384.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.532', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 532, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times C_{96}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1536.1699', 'aut_centralizer_order': 8192, 'aut_label': '384.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8192, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['128.c1', '192.c1', '192.d1'], 'contains': ['768.b1'], 'core': '384.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2790, 2790, 3689, 3689], 'generators': [388], 'label': '1536.1699.384.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '384.c1', 'normal_contained_in': ['128.c1', '192.c1', '192.d1'], 'normal_contains': ['768.b1'], 'normalizer': '1.a1', 'old_label': '384.c1', 'projective_image': '384.532', 'quotient_action_image': '1.1', 'quotient_action_kernel': '384.532', 'quotient_action_kernel_order': 384, 'quotient_fusion': None, 'short_label': '384.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '4.1', '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], [3]], '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], [2, 1, 1, 1], [4, 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], [2, 1, 1], [4, 1, 2]], 'center_label': '4.1', 'center_order': 4, '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': ['2.1', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 4, 'exponents_of_order': [2], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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, 4]], 'label': '4.1', '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': 'C4', 'ngens': 1, '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': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 4, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 3, 'number_subgroups': 3, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 1], [4, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[3]], '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': 4, 'pgroup': 2, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 5, 'gens': [1], 'pres': [2, -2, -2, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [46]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [56, 15], 'family': 'CSOPlus'}], 'GLFp': {'d': 2, 'p': 3, 'gens': [21]}, 'Perm': {'d': 4, 'gens': [22, 7]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '1536.1699', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 16, 'aut_gen_orders': [8, 16, 16, 16, 16, 8, 8, 2], 'aut_gens': [[1, 8], [1159, 188], [773, 1261], [771, 348], [583, 680], [193, 426], [1155, 189], [5, 905], [1, 1292]], 'aut_group': None, 'aut_hash': 2189271166472134719, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 16384, 'aut_permdeg': 258, 'aut_perms': 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'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': None, 'autcent_hash': 2189271166472134719, 'autcent_nilpotent': True, 'autcent_order': 16384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2.C_4^3.C_2^6.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], [2, 1, 3], [3, 1, 2], [4, 1, 12], [6, 1, 6], [8, 1, 48], [12, 1, 24], [16, 1, 64], [24, 1, 96], [32, 1, 128], [48, 1, 128], [64, 1, 256], [96, 1, 256], [192, 1, 512]], 'center_label': '1536.1699', 'center_order': 1536, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 1699, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 1, 2, 6], [6, 1, 2, 3], [8, 1, 4, 12], [12, 1, 4, 6], [16, 1, 8, 8], [24, 1, 8, 12], [32, 1, 16, 8], [48, 1, 16, 8], [64, 1, 32, 8], [96, 1, 32, 8], [192, 1, 64, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 48, 'exponent': 192, 'exponents_of_order': [9, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '128.128', 'frattini_quotient': '12.5', 'hash': 1699, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 8], [1, 8]], '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': None, 'irrep_stats': [[1, 1536]], 'label': '1536.1699', 'linC_count': None, 'linC_degree': 2, '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': True, 'monomial': True, 'name': 'C8*C192', 'ngens': 10, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 32, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 1536, 'number_divisions': 92, 'number_normal_subgroups': 164, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 164, 'number_subgroups': 164, 'old_label': None, 'order': 1536, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 12], [6, 6], [8, 48], [12, 24], [16, 64], [24, 96], [32, 128], [48, 128], [64, 256], [96, 256], [192, 512]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 16, 'outer_gen_orders': [16, 16, 8, 16, 8, 4, 8, 16], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[965, 620], [1155, 1246], [961, 1451], [963, 1496], [5, 972], [385, 526], [577, 952], [197, 11]], 'outer_group': None, 'outer_hash': 2189271166472134719, 'outer_nilpotent': True, 'outer_order': 16384, 'outer_permdeg': 258, 'outer_perms': 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46086647328856940301595938549527505850600575512302984591938131010688760373169833035906798822365529916776221442484878483951221617489730650212111051622278325744272744880614739162501985666089439594995793667910806493493530360525509748715190643655042565465013766664978845228015226563628019116765442747959644816665407287194267037548026534446661096365771137041938029915698153338412686363429607653109412273047011400469656141088513739908835733380381182515727023870113084491517054325452746023695491354354158758406316710590], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2.C_4^3.C_2^6.C_2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 75, 'pgroup': 0, 'primary_abelian_invariants': [8, 64, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 18], [8, 20], [16, 16], [32, 16], [64, 8]], 'representations': {'PC': {'code': '372826471164606928706864452580217245395969', 'gens': [1, 4], 'pres': [10, -2, -2, -2, -2, -2, -2, -2, -2, -2, -3, 20, 51, 113, 144, 175, 206, 237, 268]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [1337164603, 754851110]}, 'Perm': {'d': 75, 'gens': [34812819462234954428607685341897082192301945708552738688865836491528209085355972467097600000000, 2342588841580508410423734921329644840075247833653813500790076806185010650425874457190025134080000000000000000, 17125731743961598921943674325579392227242124480672411041416803851981460023914660624295657472000, 1001305899656801207125599609903299291487045244424726240969792252144359227041592370889603678208000000000000000, 8282187884824921168611668818381987555972846584752266182758164987540677113354309924032688179200, 330849790591367232825143178964023768926091937952705210247376975078109789451986591384082579456000000000000000, 3860415955256618126428729875983775624818504154288173718968029842331521501914651066812729456320, 1649530213841581475001430175259373643701598531447003215154104016101461640635225996085127825760, 544471857487925546941072384503952816534977960565454352280865841524404515036981945541028258664, 4]}}, 'schur_multiplier': [8], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [8, 192], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_8\\times C_{192}', 'transitive_degree': 1536, 'wreath_data': None, 'wreath_product': False}
-
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '384.532', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 8, 'aut_gen_orders': [4, 8, 8, 8, 8, 8, 2], 'aut_gens': [[1, 4], [1, 29], [291, 20], [3, 54], [99, 31], [291, 22], [193, 148], [3, 71]], 'aut_group': None, 'aut_hash': 5742833041917793096, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 66, 'aut_perms': [243189963974859202607454136997298039025663147781282029828299739771200369831293009216508488198, 410741478158499480265406375878735608760127074225021549026165854535442998319178766922279735118, 436015664375231830610752407440483091313375503543998022204554494606271290589074703624095715273, 124557387193115743098380372462655382932798198667080968568544050507406051628355686373182055309, 378266230077094113756979680964592852012550403812221274114903590528714707826815966598346360191, 526081825426694816638019697196979019228796591572160962778483511570432558495783909884534165500, 418527432415342383755063538830697719341828981890418592802625349513858138919080595273914215954], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [4, 1, 2, 2], [4, 1, 8, 1], [6, 1, 2, 1], [6, 1, 4, 1], [8, 1, 4, 2], [8, 1, 8, 1], [12, 1, 4, 2], [12, 1, 16, 1], [16, 1, 16, 2], [24, 1, 8, 2], [24, 1, 16, 1], [32, 1, 64, 1], [48, 1, 32, 2], [96, 1, 128, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2:C_2^2.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 8, 'autcent_group': None, 'autcent_hash': 5742833041917793096, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4^2:C_2^2.C_2^4', '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], [3, 1, 2], [4, 1, 12], [6, 1, 6], [8, 1, 16], [12, 1, 24], [16, 1, 32], [24, 1, 32], [32, 1, 64], [48, 1, 64], [96, 1, 128]], 'center_label': '384.532', 'center_order': 384, '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', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 532, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['32.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 1, 2, 6], [6, 1, 2, 3], [8, 1, 4, 4], [12, 1, 4, 6], [16, 1, 8, 4], [24, 1, 8, 4], [32, 1, 16, 4], [48, 1, 16, 4], [96, 1, 32, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 48, 'exponent': 96, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '32.16', 'frattini_quotient': '12.5', 'hash': 532, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 4], [1, 4]], '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, 384]], 'label': '384.532', 'linC_count': 24576, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 80, 'linQ_dim': 20, 'linQ_dim_count': 80, 'linR_count': 6144, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C4*C96', 'ngens': 8, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 32, 'number_conjugacy_classes': 384, 'number_divisions': 44, 'number_normal_subgroups': 72, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 72, 'number_subgroups': 72, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 12], [6, 6], [8, 16], [12, 24], [16, 32], [24, 32], [32, 64], [48, 64], [96, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 4, 8, 8, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[97, 188], [97, 316], [1, 164], [97, 334], [3, 53], [1, 101], [3, 381]], 'outer_group': None, 'outer_hash': 5742833041917793096, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 66, 'outer_perms': [53630740422850889539781869996511991309452617847150324426743516260302848262456023824855788940, 53630740422850889539781869996487168980889705513897549698954198310480698251398421264855788940, 485868226683065457369291729908406268166134653436958116026214435876412741479796978165663274960, 250327651002329183182592735955574769091712015224390906135607639415177460012687627603850735312, 443751737551484308291789946753026124982071032134457251652408753567631176870396938791109097570, 326919224010739911361376690922175701180225529092526528420817183229197258766247668258044832498, 25121565976239793906067627975186566614859435322008127051002397901196508880188441886719999997], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^2.C_2^4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 39, 'pgroup': 0, 'primary_abelian_invariants': [4, 32, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 10], [8, 8], [16, 8], [32, 4]], 'representations': {'PC': {'code': 74019015088146855619493121, 'gens': [1, 3], 'pres': [8, -2, -2, -2, -2, -2, -2, -2, -3, 16, 66, 91, 116, 141, 166]}, 'GLFp': {'d': 2, 'p': 97, 'gens': [15515447, 68450497]}, 'Perm': {'d': 39, 'gens': [9420320787564833044042482448295657472000, 1596595358582256025372653631463384678400000000, 4, 4553316871647675141030596900032688179200, 523394610793391012977475223548225126400000000, 2119814913695370483408246361737529456320, 903065845799780519864142501070727825760, 295496195434689904216526716510628258664]}}, 'schur_multiplier': [4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 96], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4\\times C_{96}', 'transitive_degree': 384, 'wreath_data': None, 'wreath_product': False}
