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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12335', 'ambient_counter': 12335, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12335.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.113', 'subgroup_hash': 113, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.12335', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.k1.a1', '8.k1.c1', '8.u1.a1', '8.bn1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3103, 3544, 3568, 5451, 3086, 3535, 3557, 5443], 'generators': [1, 4, 64], 'label': '256.12335.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.k1.c1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', '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': '16.10', '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, 4, 2, 4, 2, 2, 2], 'aut_gens': [[1, 2, 8], [33, 38, 44], [1, 6, 60], [5, 2, 10], [1, 6, 63], [1, 38, 15], [37, 2, 24], [1, 6, 15], [33, 34, 26]], 'aut_group': '512.10493360', 'aut_hash': 6874914387587482097, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 512, 'aut_permdeg': 32, 'aut_perms': [66102625862686814854382183546180555, 236010949604562694212383327267871336, 83821245949614352630415657958397151, 246136337988397400263347478838119375, 77015517774787155983300022643627439, 235002085785712545072172841995638770, 76184392551906758308003128219269279, 196231830971624841179491868057818082], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [4, 1, 4, 1], [4, 2, 2, 5], [8, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2:C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '4.2', 'autcentquo_hash': 2, 'autcentquo_nilpotent': True, 'autcentquo_order': 4, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [4, 1, 4], [4, 2, 10], [8, 4, 8]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '8.5', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 113, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 4], [8, 4, 2, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 168, 'exponent': 8, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '8.5', 'hash': 113, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2], 'inner_gens': [[1, 2, 44], [1, 2, 40], [37, 34, 8]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12]], 'label': '64.113', 'linC_count': 48, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 12, 'linQ_dim': 8, 'linQ_dim_count': 12, 'linR_count': 12, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.C4', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 12, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 28, 'number_divisions': 18, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 39, 'number_subgroup_classes': 55, 'number_subgroups': 73, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7], [4, 24], [8, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 1, 0, 0, 0, 0], 'outer_gens': [[1, 2, 9], [1, 6, 58], [1, 34, 24], [1, 38, 8], [1, 34, 8], [33, 2, 8]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1985188526780423877464651544814742829008285424088317476814575392989893856928648616569201, 4154112628923264636632128775345560581811008712804739481245760941829028879006354295684644, 6173192254075958537951841054780675191527474692087413872184429888595485152884157782042258, 8187884636372818974008644669228639103949846608128961376293109726798270309905592527523936, 10202480873618811639456691470785796184518652310898872541961146794314818216777211400698200, 12217075239169549674926007643948061880093513498779373956533360210631363056280464921156320], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 6]], 'representations': {'PC': {'code': 20070524782746, 'gens': [1, 2, 4], 'pres': [6, 2, 2, 2, 2, 2, 2, 31, 1059, 489, 69, 88]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 147808757934, 61179005627, 75598583751, 136653666252, 61054693752]}, 'Perm': {'d': 16, 'gens': [1596157080171, 2703006031109, 4291379339374, 3052245387364, 5598135625444, 3052245369600]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.C_4', 'transitive_degree': 32, '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': 8, 'aut_gen_orders': [4, 4, 2, 4, 8, 4, 4, 4, 2, 4], 'aut_gens': [[1, 2, 4, 32], [1, 203, 141, 48], [129, 67, 69, 240], [145, 18, 84, 224], [145, 10, 180, 224], [145, 2, 236, 176], [1, 203, 101, 112], [129, 130, 244, 240], [145, 154, 52, 224], [17, 10, 76, 96], [129, 146, 244, 112]], 'aut_group': None, 'aut_hash': 2852085768025429192, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 16384, 'aut_permdeg': 48, 'aut_perms': [7857852884473152816769549141766375936606331694368875996428981, 8197982032521063053059357610229752320570076902744831012186841, 5236521484880127917293820705649157100530077150910970092979328, 3708170807792387525827862453966863703574498936530823565058364, 8801499581918033605963095534719443418465014934638283713118917, 3719175347313586479753161315745018978830242550399355560309321, 2444157531754926539691202021547227930978275420700878579347217, 6453049884649963800544555648077639505797060261806226719026825, 5264079980552836213174432593601103453232986303005361655879628, 12333715231093605934499936696269422757824903058309354647213202], 'aut_phi_ratio': 128.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 16, 2, 1], [4, 2, 1, 2], [4, 2, 2, 2], [4, 4, 1, 3], [4, 8, 2, 2], [4, 16, 2, 1], [8, 2, 4, 1], [8, 4, 2, 3], [8, 8, 4, 1], [8, 16, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_2^7\\times C_4).C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '64.261', 'autcentquo_hash': 261, 'autcentquo_nilpotent': True, 'autcentquo_order': 64, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4\\times C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [2, 16, 2], [4, 2, 6], [4, 4, 3], [4, 8, 4], [4, 16, 2], [8, 2, 4], [8, 4, 6], [8, 8, 4], [8, 16, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.203', 'commutator_count': 1, 'commutator_label': '16.2', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 12335, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 16, 1, 2], [4, 2, 1, 4], [4, 2, 2, 1], [4, 4, 1, 3], [4, 8, 1, 4], [4, 16, 1, 2], [8, 2, 4, 1], [8, 4, 1, 2], [8, 4, 2, 2], [8, 8, 2, 2], [8, 16, 1, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 80640, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '16.14', 'hash': 12335, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 4], 'inner_gens': [[1, 130, 148, 32], [129, 2, 12, 160], [145, 26, 4, 96], [1, 130, 196, 32]], 'inner_hash': 203, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': False, 'inner_tex': 'C_2^3: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, 12], [4, 12]], 'label': '256.12335', 'linC_count': 48, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 4, 'linQ_dim': 16, 'linQ_dim_count': 6, 'linR_count': 20, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.C2^4', 'ngens': 4, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 43, 'number_conjugacy_classes': 40, 'number_divisions': 32, 'number_normal_subgroups': 107, 'number_subgroup_autclasses': 173, 'number_subgroup_classes': 308, 'number_subgroups': 807, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 39], [4, 88], [8, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 4, 2, 2, 2, 4, 2], 'outer_gen_pows': [64, 0, 0, 0, 64, 0, 0, 40], 'outer_gens': [[17, 83, 125, 48], [17, 130, 140, 96], [1, 10, 36, 96], [145, 203, 13, 224], [145, 18, 252, 224], [145, 146, 28, 112], [17, 83, 213, 112], [1, 138, 100, 32]], 'outer_group': '256.56086', 'outer_hash': 56086, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 64, 'outer_perms': [62366815264858871442033627680342351476881027472064654664462397629757642932581219523117959, 17875460920036804607970692104974004766634233278581405780116441709571788323893281273158401, 92628981258307714996124221753403227030113051932488944977033686086437076913532142559606506, 56480389892886775563537911117057502593220229252326871805064227391838652630820489966444576, 116486612268409486677099539416865199178406835480974451350059003409550345718340485161026039, 40818100627662658812177738648169399482496210083437698007405245690017328213084366540742767, 8316886030393458074154185959355354333129265401050006025974541381393563717744086356625462, 12217525275296321433558604934759368328363280379594645898872756494707196650549100642015319], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^5', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 4], [8, 3], [16, 1]], 'representations': {'PC': {'code': 10717068085596276195389256548017684974, 'gens': [1, 2, 3, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 2081, 137, 3554, 154, 66, 395, 91, 3853, 1173, 141, 2710, 166]}, 'Perm': {'d': 32, 'gens': [8303996718241738794480480261009269, 17332393113482626220418549431438842, 26330800768240160598908717985452096, 34848436254923098756425256078478842, 43299405970112730401184965616588850, 5807562520081, 51779909457930938210780067422208000, 4315608012850]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.C_2^4', 'transitive_degree': 128, '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}
