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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.16400', 'ambient_counter': 16400, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8):D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.16400.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.16400', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.h1', '4.k1', '4.l1'], 'contains': ['16.b1', '16.k1', '16.bd1', '16.bf1', '24.c1'], 'core': '8.e1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 8, 12, 32, 128], 'label': '384.16400.8.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': ['4.b1', '4.h1', '4.k1', '4.l1'], 'normal_contains': ['16.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4], [1, 2, 5], [25, 14, 44], [1, 38, 28], [1, 2, 20], [1, 27, 28], [1, 3, 4], [1, 26, 4]], 'aut_group': '128.1755', 'aut_hash': 1755, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 128, 'aut_permdeg': 10, 'aut_perms': [21025, 2810575, 374407, 1, 183120, 21288, 1270440], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 4, 1], [3, 1, 2, 1], [4, 2, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 8, 1], [12, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4:D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 4], [3, 1, 2], [4, 2, 2], [6, 1, 6], [6, 2, 8], [12, 2, 4]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 45, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 4], [3, 1, 2, 1], [4, 2, 1, 2], [6, 1, 2, 3], [6, 2, 2, 4], [12, 2, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 273, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '24.15', 'hash': 45, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 2], 'inner_gens': [[1, 2, 4], [1, 2, 28], [1, 26, 4]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 6]], 'label': '48.45', 'linC_count': 64, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 8, 'linQ_dim': 4, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6*D4', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 30, 'number_divisions': 20, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 54, 'number_subgroups': 70, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 11], [3, 2], [4, 4], [6, 22], [12, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 4, 0, 0], 'outer_gens': [[1, 2, 20], [25, 27, 20], [25, 39, 20], [25, 14, 45]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [7, 23, 5183, 15136], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 2]], 'representations': {'PC': {'code': 4858585473, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -2, -3, 217, 42, 58]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [35931072, 16563488, 7233423]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [34649835, 11532102, 34603218, 34591355, 34649828]}, 'Perm': {'d': 9, 'gens': [41040, 10824, 90744, 4, 90720]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6\\times D_4', 'transitive_degree': 24, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 2, 6, 2, 4, 12, 12, 4, 6], 'aut_gens': [[1, 2, 16, 64], [13, 226, 304, 352], [193, 10, 48, 64], [1, 6, 304, 64], [45, 46, 152, 360], [205, 198, 112, 360], [1, 206, 112, 104], [225, 238, 80, 72], [1, 202, 216, 352], [33, 194, 152, 64]], 'aut_group': None, 'aut_hash': 3261308577025293659, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 56, 'aut_perms': [484341705396059488005073872768475923474593059200456232455119852287249395739, 179162626657819837869021340444756727242168190164019301310363256021956297573, 1637933442271367539624953752965617725397160168334153307482773116193784498, 514908529310316423849961519888358000799315478922733938463993023435589933096, 664690664848662603377161840044017531084536237175621235177703824351115863309, 4240471844247381842125165227662457025429832197925186929002601915506468549, 257459063709517101987234732145409368193306171000741810538062216996119246173, 10109357680382860861551049868531941445779834551439528400485499074687189821, 70306143576842955597984821230314772965188134429384957335467800212103768339], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [2, 4, 4, 1], [2, 8, 2, 1], [2, 24, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 6, 4, 1], [4, 12, 2, 1], [4, 12, 4, 1], [6, 2, 1, 3], [6, 2, 4, 1], [6, 8, 4, 2], [8, 4, 4, 1], [8, 12, 4, 1], [12, 4, 1, 2], [12, 4, 2, 1], [24, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^9.C_2^5)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 8092891664598236742, 'autcent_nilpotent': True, 'autcent_order': 2048, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8.C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 4, 4], [2, 8, 2], [2, 24, 2], [3, 2, 1], [4, 2, 4], [4, 6, 4], [4, 12, 6], [6, 2, 7], [6, 8, 8], [8, 4, 4], [8, 12, 4], [12, 4, 4], [24, 4, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '48.38', 'commutator_count': 1, 'commutator_label': '24.9', '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': 16400, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['192.709', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 4, 1, 4], [2, 8, 1, 2], [2, 24, 1, 2], [3, 2, 1, 1], [4, 2, 1, 4], [4, 6, 1, 4], [4, 12, 1, 2], [4, 12, 2, 2], [6, 2, 1, 7], [6, 8, 1, 4], [6, 8, 2, 2], [8, 4, 2, 2], [8, 12, 2, 2], [12, 4, 1, 4], [24, 4, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 131040, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '48.51', 'hash': 16400, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 2, 3], 'inner_gens': [[1, 14, 16, 64], [5, 2, 48, 64], [1, 34, 16, 320], [1, 2, 144, 64]], 'inner_hash': 38, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': None, 'inner_tex': 'S_3\\times D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 36], [4, 14]], 'label': '384.16400', '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': '(C2*D8):D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 43, 'number_conjugacy_classes': 66, 'number_divisions': 52, 'number_normal_subgroups': 165, 'number_subgroup_autclasses': 268, 'number_subgroup_classes': 648, 'number_subgroups': 2462, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 87], [3, 2], [4, 104], [6, 78], [8, 64], [12, 16], [24, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 4, 2, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 256, 128], 'outer_gens': [[13, 238, 280, 352], [1, 6, 184, 328], [225, 42, 48, 360], [197, 238, 56, 320], [233, 194, 184, 96], [193, 6, 80, 72]], 'outer_group': None, 'outer_hash': 5432852209331838536, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 128, 'outer_perms': [202349271989831059589260375580838025726019594561240771211740204831296633476394028104213250183916702174987156736090148558852914816332746314780998805126287439574466229816762350154863279715989664318434051221308652915110, 374942209315289266820551898637324193707775823915902255863217254990356551127000267475866061553020824043484404278624171929073788323806635062566826392125831090965467368678210308177578813947919034107263466687987010946229, 17960690671077271465867628713266991223550751910278213376670741950273551008388586863441163819860788483094915351288123323325598471446295350982123123733415402441990607188079028189772429274150897340416345172741166700082, 336015066541640437472601102032443618126178038259525170573593659872872162221664525095796072098791537133800436274299325476870175100619932521189924312529290364322440171250698226736790338827114847180308296192454284645609, 47764294021080530323301405903229734037055517932725440668275685371145485108119260021153750532891422025937538379048094778234525958389882859537642559001983330241213743294078661426405260491261556353272196475196811863267, 381442838888096374325561347717780682492196557173129084668472544695857114702648189708205869678070413045182250251288598232404213114600107689537976935588422967817286337252540619683401276115959201377300869704512075905975], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^8.C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 16], [8, 4]], 'representations': {'PC': {'code': 4180357780289934973291094043907585, 'gens': [1, 2, 5, 7], 'pres': [8, -2, -2, -2, -2, -2, -2, -2, -3, 225, 41, 290, 66, 972, 116, 1158, 166, 1063]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [2543639, 2764825, 111631, 844573, 111745, 111361, 1285645, 2157163]}, 'Perm': {'d': 17, 'gens': [21197261434344, 1465, 4035192943224, 47102626007544, 2424, 69755609548800, 47102625964800, 3]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times D_8):D_6', 'transitive_degree': 192, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 84, 'aut_gen_orders': [3, 3], 'aut_gens': [[1, 2, 4], [4, 5, 3], [2, 4, 1]], 'aut_group': '168.42', 'aut_hash': 42, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 168, 'aut_permdeg': 7, 'aut_perms': [4361, 244], 'aut_phi_ratio': 42.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PSL(2,7)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '168.42', 'autcent_hash': 42, 'autcent_nilpotent': False, 'autcent_order': 168, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\PSL(2,7)', '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, 7]], 'center_label': '8.5', 'center_order': 8, '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'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [3], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '8.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 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, 8]], 'label': '8.5', 'linC_count': 28, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 28, 'linQ_dim': 3, 'linQ_dim_count': 28, 'linR_count': 28, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 8, 'number_divisions': 8, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [3, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[4, 5, 3], [2, 4, 1]], 'outer_group': '168.42', 'outer_hash': 42, 'outer_nilpotent': False, 'outer_order': 168, 'outer_permdeg': 7, 'outer_perms': [4361, 244], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\PSL(2,7)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3], 'pres': [3, -2, 2, 2]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [16482, 16322, 3362]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [8156, 13286, 13933]}, 'Perm': {'d': 6, 'gens': [120, 6, 1]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
