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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47306', 'ambient_counter': 47306, 'ambient_order': 1728, 'ambient_tex': 'C_{12}.D_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47306.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.710', 'subgroup_hash': 710, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.47306', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': ['432.o1', '432.n1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1', '2.h1'], 'contains': ['8.e1', '8.h1', '8.w1', '12.j1', '12.bv1', '12.bx1', '12.by1'], 'core': '4.o1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [20625575, 476581, 11863825, 25151309, 28952407, 2376551, 714910], 'label': '1728.47306.4.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1', 'normal_contained_in': ['2.b1', '2.c1', '2.h1'], 'normal_contains': ['8.e1', '8.h1', '8.w1', '12.j1'], 'normalizer': '1.a1', 'old_label': '4.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', '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': 5, 'aut_exponent': 24, 'aut_gen_orders': [6, 6, 8, 12, 8, 6], 'aut_gens': [[1, 6, 36], [139, 366, 180], [313, 30, 282], [113, 378, 60], [197, 246, 258], [263, 294, 120], [341, 222, 276]], 'aut_group': None, 'aut_hash': 1981728487577310646, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 55296, 'aut_permdeg': 74, 'aut_perms': [289202597730844605345254472016867252345517428181146876338025768118499365392884423401993354152444831727831878, 16690924429612316787592004872088922017324932154100766668130487799459326164069318357984150774269607150562575, 248608013283912708598694168369585161101867592624565697884005377622055951035530446685803411024494081684115831, 154979475411581874364733104485416290902276216625532090287615344076118697641181625521655233328163034287588136, 296045818925215521442492256435706494593424258851728240664187294352382356968806219541983783566411636044587626, 83550941638718536550937148850850960453619139769828095940557922197601508065368500950443007397521842741485466], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [3, 2, 4, 1], [3, 2, 8, 1], [4, 2, 2, 1], [4, 18, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 4, 1], [6, 2, 8, 2], [6, 2, 16, 1], [12, 2, 4, 1], [12, 2, 16, 1], [12, 2, 32, 1], [12, 18, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '\\ASL(2,3).C_2^6.C_2^2', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '864.4661', 'autcentquo_hash': 4661, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [3, 2, 12], [4, 2, 2], [4, 18, 4], [6, 1, 6], [6, 2, 36], [12, 2, 52], [12, 18, 8]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '36.13', 'commutator_count': 1, 'commutator_label': '18.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 710, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['72.31', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 2, 1, 4], [3, 2, 2, 4], [4, 2, 1, 2], [4, 18, 1, 4], [6, 1, 2, 3], [6, 2, 1, 12], [6, 2, 2, 12], [12, 2, 2, 10], [12, 2, 4, 8], [12, 18, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 273, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '216.175', 'hash': 710, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 6], 'inner_gens': [[1, 30, 396], [13, 6, 36], [73, 6, 36]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 36, 'inner_split': False, 'inner_tex': 'C_6:S_3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 102]], 'label': '432.710', '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': 'C6^2.D6', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 126, 'number_divisions': 68, 'number_normal_subgroups': 118, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 292, 'number_subgroups': 708, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 26], [4, 76], [6, 78], [12, 248]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 8, 4, 8, 6], 'outer_gen_pows': [156, 300, 0, 156, 0, 0], 'outer_gens': [[139, 366, 180], [313, 30, 282], [113, 378, 60], [197, 246, 258], [263, 294, 120], [341, 222, 276]], 'outer_group': '1536.408635824', 'outer_hash': 4361138917581321938, 'outer_nilpotent': False, 'outer_order': 1536, 'outer_permdeg': 128, 'outer_perms': [3013996162416681768042917781819666330908132057618533083474088672938774731744530938328663095714437662106285035527107344390153526744651386811939606012664507503094734389494800261398535896527095068545907466109876307172, 96412857804515824613397751987226348538534150841118040115642135831138758217863950610930160594050327962252122373651906938943753494956757608693799127364749986248122485300925232374227464473776547471570542862502367570, 6145644317959760679442795829445079884971123932154053097194719363027716455797502885529066309267979701949620185927932100724643162391804476717258103517990818784544137262738142287424090194173128184490876260057426564386, 9182215938593140051337317653877080774975160319935991362864881490153171922676533717699592358559490177761516060870516246909568098524527854705945829230937335462388645559522650768660422102484813358176963304087595770267, 12218787379698222263269151349772341561324230376292945512912616885597089189635953991395976920364067056612479342230891805216179537340439395603310984883808551556804249207618778725883160744743948848370963340291149286544, 9158848162905106420871238950954054754742836600874511300916847031678847065832954544621291406133805682525128675127582711647990319391546512401663673989662810798909426167280201823494150854512134322057924109401211603643], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\SL(2,3).C_2^5.C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 26], [4, 26], [8, 8]], 'representations': {'PC': {'code': 9044638282289587771387277457480617, 'gens': [1, 3, 5], 'pres': [7, -2, -3, -2, -3, -2, -2, -3, 14, 1520, 632, 58, 675, 13864, 102, 15125, 124, 14118]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1166425, 793169, 1632995, 1614733, 1197961, 1001697, 1033970]}, 'Perm': {'d': 19, 'gens': [356995585558080, 1307682729600, 12511680, 3, 8361600, 6706022400, 6758073587865600]}}, 'schur_multiplier': [2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.D_6', 'transitive_degree': 144, '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [12, 4, 4, 4, 12, 4, 12, 12], 'aut_gens': [[476189, 477151, 6884099, 20630281, 28000481], [478217, 36544067, 6884099, 17929459, 28000481], [717469, 11866349, 25155365, 15278153, 9020737], [717469, 36545029, 25155365, 32438273, 5222015], [11867311, 25156897, 25153337, 23564986, 17560315], [25156897, 19221994, 18273371, 5591081, 17560315], [11868377, 36544067, 6884099, 9345187, 3323803], [18273776, 25156897, 25155365, 11226686, 33697415], [25153907, 36540973, 25155365, 25209092, 17560315]], 'aut_group': '7776.be', 'aut_hash': 8868945092102083686, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 442368, 'aut_permdeg': 48, 'aut_perms': [6339448440660071912076207785706630663360896050876438869531840, 2050195056120813762650790115646974489353801498463329309414346, 11461376706139929060489894071264725735796964182838140683850545, 4621675196675612054099332322086727241066430058648151832059634, 5724006481603863925737057285918164130859269216239044980287744, 3713410702745383308830594688322256546316863102165873615526265, 9649478869123326844887165102408365928040368801335288947733245, 6675263472799903861119938564150876307810516626940517022630223], 'aut_phi_ratio': 768.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 4, 2], [2, 9, 4, 1], [2, 54, 4, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 4, 2, 1], [3, 8, 1, 1], [4, 2, 2, 1], [4, 3, 8, 1], [4, 18, 2, 1], [4, 18, 8, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 2, 4, 1], [6, 4, 1, 1], [6, 4, 2, 2], [6, 4, 4, 1], [6, 6, 8, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 12, 4, 1], [6, 12, 8, 2], [6, 18, 4, 1], [6, 24, 4, 1], [12, 2, 4, 1], [12, 4, 4, 1], [12, 4, 8, 1], [12, 6, 8, 2], [12, 8, 2, 1], [12, 8, 4, 1], [12, 12, 8, 1], [12, 18, 4, 1], [12, 36, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3^4:S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '512.6249567', 'autcent_hash': 6452065007057432321, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '864.4686', 'autcentquo_hash': 4686, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^3:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 8], [2, 9, 4], [2, 54, 4], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 2, 2], [4, 3, 8], [4, 18, 10], [6, 2, 9], [6, 4, 9], [6, 6, 8], [6, 8, 3], [6, 12, 20], [6, 18, 4], [6, 24, 4], [12, 2, 4], [12, 4, 12], [12, 6, 16], [12, 8, 6], [12, 12, 8], [12, 18, 4], [12, 36, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '432.759', 'commutator_count': 1, 'commutator_label': '54.15', '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': 47306, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['864.4355', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 8], [2, 9, 1, 4], [2, 54, 1, 4], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 1, 2], [4, 3, 2, 4], [4, 18, 1, 10], [6, 2, 1, 9], [6, 4, 1, 9], [6, 6, 2, 4], [6, 8, 1, 3], [6, 12, 1, 12], [6, 12, 2, 4], [6, 18, 1, 4], [6, 24, 1, 4], [12, 2, 2, 2], [12, 4, 1, 4], [12, 4, 2, 4], [12, 6, 2, 8], [12, 8, 1, 2], [12, 8, 2, 2], [12, 12, 2, 4], [12, 18, 2, 2], [12, 36, 1, 8]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 9999360000, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4704', 'hash': 47306, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 3, 6, 6], 'inner_gens': [[476189, 477151, 6884099, 29203867, 28000481], [476189, 477151, 25391588, 29205895, 28000481], [476189, 717469, 6884099, 20630281, 28000481], [11864321, 11867311, 6884099, 20630281, 19460903], [476189, 477151, 6884099, 26507413, 28000481]], 'inner_hash': 759, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': False, 'inner_tex': 'C_2\\times S_3^3', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 72], [4, 48], [8, 10]], 'label': '1728.47306', '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': 'C12.D6^2', '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': 42, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 162, 'number_divisions': 128, 'number_normal_subgroups': 668, 'number_subgroup_autclasses': 700, 'number_subgroup_classes': 4178, 'number_subgroups': 31540, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 303], [3, 26], [4, 208], [6, 534], [12, 656]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 2, 4], 'outer_gen_pows': [474553, 474553, 474553, 474553, 22306289, 474553], 'outer_gens': [[36544067, 476189, 36544637, 3710128, 31799203], [25153907, 25154869, 25153337, 33785642, 3323803], [25153907, 36545029, 25153337, 20866504, 5222015], [25153907, 11866349, 25153337, 27616453, 3323803], [36545029, 25153907, 25391588, 9347215, 28000481], [25154869, 477151, 18273371, 20630281, 28000481]], 'outer_group': '7776.cp', 'outer_hash': 2734666131921231189, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 16, 'outer_perms': [3165249870072, 374659106873, 6557136755683, 1508455906586, 6819107075526, 9697035398665], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3^2:S_3^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 48], [4, 28], [8, 14], [16, 6]], 'representations': {'PC': {'code': 3698911848691991278430874763685306070689642047449129, 'gens': [1, 2, 3, 5, 7], 'pres': [9, -2, -2, -2, -3, -2, -3, -2, -2, -3, 281, 74, 300, 44284, 19993, 130, 5189, 4200, 186, 4363, 214, 3932]}, 'GLZN': {'d': 2, 'p': 78, 'gens': [476581, 11863825, 477151, 28948351, 25151309, 22308073, 20626225, 14714185, 714910]}, 'Perm': {'d': 19, 'gens': [356995106103600, 1308153455304, 1307682734665, 1307678087544, 12506424, 3719544, 6706022400, 6758061133824000, 3]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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_{12}.D_6^2', 'transitive_degree': 96, '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': '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}
