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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.46623', 'ambient_counter': 46623, 'ambient_order': 512, 'ambient_tex': 'C_8^2:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.46623.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.4980', 'subgroup_hash': 4980, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times C_8).C_2^3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '512.46623', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bvl', 'aut_weyl_index': 2, 'centralizer': '256.a1.a1', 'complements': ['256.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.e1.b1', '4.s1.a1', '4.u1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3590, 5063, 6340, 4634, 3596, 5276, 6326, 4718], 'generators': [1, 4, 352], 'label': '512.46623.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.e1.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '256.2416', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '256.2416'}
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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': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 8, 4, 2, 4, 4, 4, 2], 'aut_gens': [[1, 2, 4, 32], [129, 210, 199, 72], [209, 234, 252, 32], [209, 58, 167, 216], [129, 66, 172, 96], [129, 194, 84, 32], [129, 82, 196, 32], [1, 82, 20, 160], [1, 130, 213, 240]], 'aut_group': '4096.bvl', 'aut_hash': 1240052989601480040, 'aut_nilpotency_class': 5, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 128, 'aut_perms': [77019068000186427908110879643138126579626532186760233348597975429792023181534920446914438260843691579682125720274488041951331902126012629512893302169936432425898154703259324497093502897575291404176398960872639926222, 75162824506675687044808900755520221286059812104782844727028571142876359133315616293954798669413268937491878198436587631695463495472352571330946686353345870747564994435776317416678149852613109241893621321534595406236, 355146167828984440107731481709165112122279745846376292470835857291688614898371249103789481067309375242454346174255657295021367213592358089327416953673223904561898790996272719703052901750033437695522362409484769525503, 74411708922538066347738554833839612254476076138375552115935441269571583630553886943429230231476294087233880809497157475684249505446094454923553616417800545340324045329714582305893352442178688780759362163271909926451, 229293258727874599830402788237272711504823363462244407315398141766399852958223146095518672678218138575145347896120395887987095122666009046622296557999808754986864962312188541430435032118202264083797013594844128360762, 195659542855557556546859718610447640977514192689158070559690602964115066601026082499856917591654789733814950623529036372360225284260261518837104155898128283165771192529877036286258843141004873191974655500102875253738, 363743049350404867977031952670235992554767271874824110924975768084100244486219030794881383892782036626168974020156207037392086398456232468678083333889759861384432722073824010288009974524676275285163863006090558979200, 383325016052323527256233794978234469855277540884274632526430094574402063714395154527835383479059279901272250347929599503415588469439129032863104257525143407900633681499661815813778475824080174471778784160086324113059], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 16, 1, 3], [4, 2, 2, 1], [4, 4, 1, 1], [4, 4, 2, 1], [4, 8, 1, 1], [4, 16, 1, 1], [8, 4, 4, 1], [8, 8, 2, 1], [16, 16, 8, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_2\\times D_4^2).C_2^5', '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': 4, 'autcentquo_group': '512.6377421', 'autcentquo_hash': 6278707548141476792, 'autcentquo_nilpotent': True, 'autcentquo_order': 512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4.C_2^5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 16, 3], [4, 2, 2], [4, 4, 3], [4, 8, 1], [4, 16, 1], [8, 4, 4], [8, 8, 2], [16, 16, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.287', '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': 4980, '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], [2, 4, 1, 1], [2, 16, 1, 3], [4, 2, 1, 2], [4, 4, 1, 3], [4, 8, 1, 1], [4, 16, 1, 1], [8, 4, 1, 4], [8, 8, 1, 2], [16, 16, 2, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1344, 'exponent': 16, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 2]], 'familial': False, 'frattini_label': '32.3', 'frattini_quotient': '8.5', 'hash': 4980, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [2, 2, 8, 4], 'inner_gens': [[1, 2, 212, 160], [1, 2, 60, 224], [209, 106, 4, 224], [129, 66, 68, 32]], 'inner_hash': 287, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'C_4^2.D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 4], [4, 6], [8, 2]], 'label': '256.4980', 'linC_count': 2, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C4*C8).C2^3', 'ngens': 3, 'nilpotency_class': 4, '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': 15, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 28, 'number_divisions': 24, 'number_normal_subgroups': 49, 'number_subgroup_autclasses': 124, 'number_subgroup_classes': 206, 'number_subgroups': 815, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 55], [4, 40], [8, 32], [16, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 80, 0, 0], 'outer_gens': [[1, 2, 7, 200], [1, 2, 5, 112], [1, 2, 12, 32], [1, 210, 4, 160], [129, 2, 4, 32]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 4, '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, 8], [4, 6], [8, 2]], 'representations': {'PC': {'code': 180499410654030955351605315075232627968953212, 'gens': [1, 2, 3, 6], 'pres': [8, -2, 2, 2, -2, -2, 2, -2, -2, 5090, 730, 66, 4355, 2443, 91, 2892, 356, 7685, 5389, 2709, 141, 5390, 2710, 166]}, 'Perm': {'d': 16, 'gens': [20916435456000, 6354396736, 1313901393960, 1313941680137, 9703614452976, 4097506706057, 5167, 1313941673647]}}, 'schur_multiplier': [2, 4], '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\\times C_8).C_2^3', 'transitive_degree': 16, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 4, 4, 4, 4, 2, 8, 4], 'aut_gens': [[1, 4, 8, 64], [19, 4, 72, 448], [385, 4, 136, 320], [353, 36, 488, 480], [209, 436, 280, 192], [417, 388, 8, 64], [421, 36, 280, 336], [481, 276, 8, 64], [385, 36, 296, 320]], 'aut_group': '8192.xo', 'aut_hash': 2168597184236359916, 'aut_nilpotency_class': 5, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 96, 'aut_perms': [93741476579761360608155174069961040087624194963323862163165722750288027753985207115164032743281286816910958221177343596290977995830057342403445701169, 20877430344528908280278972429867141921900560359593380488533823974144110910077774768255422920778371011008154844441020464820269045514940466652851825934, 501333087093278132460149858408242185556878112053935600169195269514396479183066419069941331099395843169562534496394779123393232439772675352700817538015, 146596812221985900086536214793545782484343348382921904956549512563588579786837440222213475525408016412320219855612208790578591510694096514533502668129, 511554319534872360802561596648689074672673559328731369870233010258839415469803081950888325051421166462325456132454341828772988134300199357341094974182, 840410690549992511421558659481651777376259373903528407600080120940352003263884209715373851778155778658402080224503090078564125495493999736897391453213, 197809455044917765051774933785953655247614693773662613033261802032889993306681102533927575155677793758426824442473432665862739619413568560232747106650, 10439878843727752031817340518193137965487436365495023745800327431936332516370808723699466109307103151926693450373518902177406819151162018813933657021], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 16, 1, 3], [2, 32, 1, 1], [4, 2, 2, 1], [4, 4, 1, 1], [4, 4, 2, 1], [4, 8, 1, 1], [4, 16, 1, 1], [4, 16, 4, 1], [4, 32, 1, 1], [8, 8, 2, 2], [8, 8, 4, 1], [8, 16, 2, 1], [8, 16, 4, 1], [16, 32, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_2^2\\times D_4^2).C_2^5', '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': 4, 'autcentquo_group': None, 'autcentquo_hash': 8719009971623998540, 'autcentquo_nilpotent': True, 'autcentquo_order': 1024, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times C_2^6.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 16, 3], [2, 32, 1], [4, 2, 2], [4, 4, 3], [4, 8, 1], [4, 16, 5], [4, 32, 1], [8, 8, 8], [8, 16, 6], [16, 32, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '256.2416', 'commutator_count': 1, 'commutator_label': '32.3', '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', '2.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 46623, '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], [2, 4, 1, 1], [2, 16, 1, 3], [2, 32, 1, 1], [4, 2, 1, 2], [4, 4, 1, 3], [4, 8, 1, 1], [4, 16, 1, 1], [4, 16, 2, 2], [4, 32, 1, 1], [8, 8, 1, 8], [8, 16, 1, 2], [8, 16, 2, 2], [16, 32, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 5376, 'exponent': 16, 'exponents_of_order': [9], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 4]], 'familial': False, 'frattini_label': '64.85', 'frattini_quotient': '8.5', 'hash': 46623, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [8, 2, 8, 4], 'inner_gens': [[1, 20, 360, 224], [49, 4, 56, 448], [225, 20, 8, 64], [417, 132, 8, 64]], 'inner_hash': 2416, 'inner_nilpotent': True, 'inner_order': 256, 'inner_split': False, 'inner_tex': 'C_4^2.(C_2\\times D_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 12], [4, 4], [8, 6]], 'label': '512.46623', 'linC_count': 4, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C8^2:(C2*C4)', 'ngens': 3, 'nilpotency_class': 4, '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': 21, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 38, 'number_divisions': 32, 'number_normal_subgroups': 60, 'number_subgroup_autclasses': 261, 'number_subgroup_classes': 402, 'number_subgroups': 2026, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 87], [4, 136], [8, 160], [16, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [16, 0, 66, 32], 'outer_gens': [[435, 276, 8, 352], [33, 4, 8, 64], [421, 388, 408, 336], [147, 308, 136, 96]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [16703, 16, 15960, 6480], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 4, '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, 12], [4, 6], [8, 6]], 'representations': {'PC': {'code': '103449793541506701523162071180323865332143141845343598070169307', 'gens': [1, 3, 4, 7], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 3754, 542, 2225, 12963, 732, 525, 102, 6484, 562, 130, 15557, 14118, 10095, 7080, 186, 27655, 6937, 214]}, 'Perm': {'d': 16, 'gens': [15316467690942, 15310288183680, 5612501687742, 6920263158463, 11657, 8402167094393, 1313941668480, 4097506710982, 1313941673647]}}, 'schur_multiplier': [2, 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_8^2:(C_2\\times C_4)', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'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}
