-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.3981', 'ambient_counter': 3981, 'ambient_order': 384, 'ambient_tex': 'C_2\\times C_{48}.C_4', 'central': True, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '384.3981.192.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.65', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 65, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{48}.C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '384.3981', 'aut_centralizer_order': 6144, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '1.a1.a1', 'complements': ['2.c1.b1', '2.c1.c1', '2.c1.a1', '2.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.b1', '96.a1.a1', '96.h1.b1'], 'contains': ['384.a1.a1'], 'core': '192.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [733, 1419, 1043, 9127, 2007, 2183, 1725, 8309], 'generators': [193], 'label': '384.3981.192.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.b1', 'normal_contained_in': ['64.a1.b1', '96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.b1', 'projective_image': '192.65', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.65', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', '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': [[1]], '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], [2, 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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, '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'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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': 48, 'aut_gen_orders': [4, 16, 8, 12, 24, 4, 12, 16], 'aut_gens': [[1, 2, 8], [1, 123, 377], [193, 15, 136], [1, 26, 280], [1, 70, 344], [1, 214, 200], [1, 166, 40], [193, 323, 8], [193, 271, 297]], 'aut_group': None, 'aut_hash': 3825274906933175302, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 192, 'aut_perms': [150540746723445026248266883276742997604533378355426695034252141433304833467173971976318767724084066064586658770046187713279785177174429978739615544093120881958739294350593553862046935884067506438715615156087548412285233855712467672462831170002268278251012441697236329636609784797862453529624845321692804228448095054351704955686913296033877078061131362017495, 53798374508250947208572486703207108557750342527640613894437534975995573256650638208354572637182699029848216091420165233839301668234946707887745052974752120394209852532135993331276012910042953207731039054970833804889791231111010631871798963700652706053431551879217229321290732244668096278088817563016903770851568450817850861769285958947435717373917041757914, 297381049210084215979910275205556933750301510237375608226193527347102482253133415060163966663881910476638240329751090570500592108852662762747652902343706219376321592048152872687647720487842568614553954934060850599489359907803202039663590112197422464486026482222798712638837141948176099470500735416804537041754215927137800081696746372215770557554155571407664, 9309038946834051609723755585639259095696667147907438329063082234119648501134463400143124533307534612208731529491932005730698755995163151462075688102223553762535584383267825174293391709823086763471990184431718638117660430246178569063471454901908281701364069640112657853354030677945716607282193507413956421413866277404471554285435388674657279712531888139520, 174726392820775221691606028539423502266748967634881396064432104707637505549740435639927649645513805261563936407311332638877180967189314019400769089568850861647578768928531440994647075650361371259358872270545338619954089031029197074348981536224424587190752010597911994409743333911164865163107835253792951233165955990588585738449842862610736763342419151215936, 217469063538492261109090514178688230940283634128663456371775613990503541373401124115195525847762550393309031786197764582316655977199356524766390458174384274309267760366390580692956847272917499642501712957103575420452615440499270871432706026511417553367375427996863408461686369853710409236231177428115245063925801001807791708012862816918997013224767528399008, 284621158673399220838508821520430826963061110062967258529879378718104455779945492484095329234772301587859362418873599112187101148939913682543056758929916246832051133129835784166102615689373107172931424032122015341109146936766442203943526475334212301623691976411757434155146874713925586671446116584943300059625434520402545511736846241746601469132044076124136, 24280857181641526186472552905074838068698087606773108469144275029399527049392236432398118326324434195553589401567439113132254660795807814263512138019504177549842759414951869231692521867729557065509012556903765438956460768921189883878793609384644972720390084113761351353837663136280176941558846874998476752617149508099789527993398863642227129774880586469426], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [3, 2, 1, 1], [4, 1, 2, 2], [4, 2, 1, 2], [6, 2, 1, 1], [6, 2, 2, 3], [8, 2, 2, 4], [8, 24, 8, 1], [12, 2, 2, 4], [16, 2, 8, 2], [24, 2, 4, 4], [48, 2, 16, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^2\\times (C_2^2\\times C_8).C_2^5)', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '192.1331', 'autcentquo_hash': 1331, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_8:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [3, 2, 1], [4, 1, 4], [4, 2, 2], [6, 2, 7], [8, 2, 8], [8, 24, 8], [12, 2, 8], [16, 2, 16], [24, 2, 16], [48, 2, 32]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '48.7', 'commutator_count': 1, 'commutator_label': '24.2', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3981, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['192.65', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [3, 2, 1, 1], [4, 1, 2, 2], [4, 2, 1, 2], [6, 2, 1, 3], [6, 2, 2, 2], [8, 2, 2, 4], [8, 24, 2, 4], [12, 2, 2, 4], [16, 2, 4, 4], [24, 2, 4, 4], [48, 2, 8, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 48, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.5', 'frattini_quotient': '24.14', 'hash': 3981, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [1, 2, 24], 'inner_gens': [[1, 2, 8], [1, 2, 184], [1, 210, 8]], 'inner_hash': 7, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': False, 'inner_tex': 'D_{24}', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 92]], 'label': '384.3981', 'linC_count': 256, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 8, 'linQ_dim': 18, 'linQ_dim_count': 4, 'linR_count': 64, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C48.C4', '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': 31, 'number_characteristic_subgroups': 63, 'number_conjugacy_classes': 108, 'number_divisions': 40, 'number_normal_subgroups': 93, 'number_subgroup_autclasses': 98, 'number_subgroup_classes': 144, 'number_subgroups': 334, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 8], [6, 14], [8, 208], [12, 16], [16, 32], [24, 32], [48, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4, 4], 'outer_gen_pows': [0, 0, 120, 0, 144, 0], 'outer_gens': [[1, 51, 56], [1, 6, 248], [193, 223, 8], [193, 6, 56], [1, 26, 297], [1, 51, 152]], 'outer_group': '256.55647', 'outer_hash': 55647, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 16, 'outer_perms': [5041, 1321086780720, 5046, 998282880, 9696556765129, 2884555260720], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 37, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 8], [8, 4], [16, 2], [32, 2]], 'representations': {'PC': {'code': 616414536044448451686613617144359845377, 'gens': [1, 2, 4], 'pres': [8, -2, -2, -2, -2, -2, -2, -2, -3, 41, 1170, 2955, 91, 7372, 116, 8461, 141, 8974, 166, 8207]}, 'GLZN': {'d': 2, 'p': 51, 'gens': [663299, 3316294, 133519, 1724476, 2122432, 2272696, 132667, 5040776]}, 'GLZq': {'d': 2, 'q': 64, 'gens': [5539357, 4456465, 7370083, 15139881, 8783873, 12320815, 825917, 8650785]}, 'Perm': {'d': 37, 'gens': [416038858982680599333837421099008765458407, 809027418835619028664739577670371086436480, 1191563031444630473069689532209567074640081, 1574304021031944922179648511731712934077440, 1956850380399224542523750884208655980610480, 2329137337065122634541093534336854005098800, 1191563031444630473069689532209567074640080, 30]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{48}.C_4', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 48, 'aut_gen_orders': [2, 2, 2, 4, 48], 'aut_gens': [[1, 4], [3, 100], [1, 68], [109, 188], [169, 44], [77, 4]], 'aut_group': '1536.230683028', 'aut_hash': 8779664174755546961, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 21, 'aut_perms': [1, 6, 17566011496111166646, 15000853136486968806, 10508941326955237230], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1], [8, 2, 2, 2], [8, 24, 4, 1], [12, 2, 2, 2], [16, 2, 4, 2], [24, 2, 4, 2], [48, 2, 8, 2]], 'aut_supersolvable': True, 'aut_tex': 'D_6\\times D_{16}:C_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '192.1331', 'autcentquo_hash': 1331, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_8:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [3, 2, 1], [4, 1, 2], [4, 2, 1], [6, 2, 3], [8, 2, 4], [8, 24, 4], [12, 2, 4], [16, 2, 8], [24, 2, 8], [48, 2, 16]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '48.7', 'commutator_count': 1, 'commutator_label': '24.2', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 65, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1], [8, 2, 2, 2], [8, 24, 2, 2], [12, 2, 2, 2], [16, 2, 4, 2], [24, 2, 4, 2], [48, 2, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 48, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 16]], 'familial': False, 'frattini_label': '16.5', 'frattini_quotient': '12.4', 'hash': 65, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 24], 'inner_gens': [[1, 92], [105, 4]], 'inner_hash': 7, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': False, 'inner_tex': 'D_{24}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 46]], 'label': '192.65', 'linC_count': 16, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 4, 'linQ_dim': 18, 'linQ_dim_count': 2, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C48.C4', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 19, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 54, 'number_divisions': 20, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 34, 'number_subgroup_classes': 40, 'number_subgroups': 88, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [6, 6], [8, 104], [12, 8], [16, 16], [24, 16], [48, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 60, 0], 'outer_gens': [[3, 4], [1, 28], [13, 4], [1, 148]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 4], [8, 2], [16, 1], [32, 1]], 'representations': {'PC': {'code': 1181929598271331148122060380168065, 'gens': [1, 3], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 14, 680, 1934, 58, 5155, 80, 6164, 102, 6725, 124, 6278]}, 'GLFp': {'d': 2, 'p': 97, 'gens': [11543, 87616609, 60236443]}, 'Perm': {'d': 35, 'gens': [315020797296331646918615236130521602241, 645281784668631175692030067221227990880, 949420623217391539478097555887055738984, 1253671306282987188392545345199804029344, 1540370342827916708849695444873770235704, 1853275604215155380388220644227032279224, 3]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{48}.C_4', 'transitive_degree': 96, 'wreath_data': None, 'wreath_product': False}
