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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '78804.b', 'ambient_counter': 2, 'ambient_order': 78804, 'ambient_tex': 'C_{398}:C_{198}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 13134, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '78804.b.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '13134.f', 'subgroup_hash': 12, 'subgroup_order': 13134, 'subgroup_tex': 'C_{199}:C_{66}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '78804.b', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13134.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.b1.b1', '66.b1.b1', '1194.b1.b1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4473, 7331, 3724, 7828, 3303, 7526, 3008, 3246], 'generators': [297, 132, 396, 18], 'label': '78804.b.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.b1.b1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '18.b1.b1', '66.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '26268.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '13134.h'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '66.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 39402, 'aut_gen_orders': [198, 398], 'aut_gens': [[1, 22], [1, 12496], [8977, 4400]], 'aut_group': '78804.a', 'aut_hash': 1732360149213810607, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 78804, 'aut_permdeg': 201, 'aut_perms': [7844765794801755003323891217213786104500286325232778825737630311203202404850187064785395461078108897743163910941402173937572581043336717191733551683006435433818603880831873985800142390645654421690299127723513071931862347673132765079843083405686019779497320988713910073232164854718126143953689530991100795370986031405739191593521697268170391131707501096317508861440940136140609, 127610229096837571379784503460062648927393768117326363189564907280347054450802612278184810282119171816925360914140868304740257817637875082353981431799087995729482947593308312562139980966403722021025855999026905227035138573993184533834909038697328358623728369855844896624629934853661417086512521719895007042556437492798849398164909667418837403746966116579782032254878727783477421], 'aut_phi_ratio': 19.9, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 199, 1, 1], [3, 1, 2, 1], [6, 199, 2, 1], [11, 199, 1, 10], [22, 199, 1, 10], [33, 199, 2, 10], [66, 199, 2, 10], [199, 22, 9, 1], [597, 22, 18, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times F_{199}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 39402, 'autcentquo_group': '39402.d', 'autcentquo_hash': 6821401462869295210, 'autcentquo_nilpotent': False, 'autcentquo_order': 39402, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{199}', 'cc_stats': [[1, 1, 1], [2, 199, 1], [3, 1, 2], [6, 199, 2], [11, 199, 10], [22, 199, 10], [33, 199, 20], [66, 199, 20], [199, 22, 9], [597, 22, 18]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '4378.a', 'commutator_count': 1, 'commutator_label': '199.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '3.1', '11.1', '199.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['4378.a', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 199, 1, 1], [3, 1, 2, 1], [6, 199, 2, 1], [11, 199, 10, 1], [22, 199, 10, 1], [33, 199, 20, 1], [66, 199, 20, 1], [199, 22, 9, 1], [597, 22, 18, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1440, 'exponent': 13134, 'exponents_of_order': [1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 11, 199], 'factors_of_order': [2, 3, 11, 199], 'faithful_reps': [[22, 0, 18]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '13134.f', 'hash': 12, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4378, 'inner_gen_orders': [22, 199], 'inner_gens': [[1, 10384], [2773, 22]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 4378, 'inner_split': True, 'inner_tex': 'C_{199}:C_{22}', 'inner_used': [1, 2], 'irrC_degree': 22, 'irrQ_degree': 396, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 66], [22, 27]], 'label': '13134.f', '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': True, 'monomial': True, 'name': 'C199:C66', 'ngens': 4, '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': 46, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 93, 'number_divisions': 10, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 16, 'number_subgroups': 1204, 'old_label': None, 'order': 13134, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 199], [3, 2], [6, 398], [11, 1990], [22, 1990], [33, 3980], [66, 3980], [199, 198], [597, 396]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 18, 'outer_gen_orders': [18], 'outer_gen_pows': [18], 'outer_gens': [[1, 9086]], 'outer_group': '18.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 18, 'outer_permdeg': 11, 'outer_perms': [3859800], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{18}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 202, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 2], [10, 2], [20, 2], [198, 1], [396, 1]], 'representations': {'PC': {'code': '31370899927240120358130079340545055', 'gens': [1, 3], 'pres': [4, -2, -11, -3, -199, 8, 124610, 13602, 46, 78147, 54391]}, 'GLFp': {'d': 2, 'p': 199, 'gens': [7880799, 1040239127]}, 'Perm': {'d': 202, 'gens': [788717715775379712147044883354113803238779741712176774503593236359568043071535222678707832421615822549229750026246094776642794817601281250418805260077961068512740531321929441349809910248430158712002445828331447620399662889469470639504688903718292949569357677734702193391481020240952428847333079808817352115455206255835073607377287982653800782681422860939486823694278550669400, 3, 1593208585881059268929057010943344089257063492719445276108336696961159274386117195065000839039811462843456833185122103754109056016938679434804905286969248996260524755514005102279076618054585461070075195745437159037499059518252028715592436547845006513606523826229209705152575722736980854632055061530519335153281496082300365554908606411574913297154440143419164768100521951480680, 160886344556907055407607556799828226265389254239163704741381840835073325819198754993630057919500682366731012489348152972582074037157462508083173024454589007206100945501648888505849401735727064108564272273717902269077863438899795538499179779467359841236424207725331370859648977133918159472474224866790854724954885160396513494173529641548264809950635855884474746935175522182136560]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [66], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{199}:C_{66}', 'transitive_degree': 597, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '396.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 39402, 'aut_gen_orders': [198, 1194], 'aut_gens': [[1, 198], [39403, 26334], [43825, 198]], 'aut_group': '236412.a', 'aut_hash': 2102602887211588400, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 236412, 'aut_permdeg': 995, 'aut_perms': [1235492412716142312487181621151421558325539570428719166460926876361483426676363525007779950887176618371049753947560424045886337267019079789228606577512966502935002272832324235796097615585427481602866648811798176629509035672809375241589425760621683686871658528884072813497842338096262949140138632561620846820902625394370531244498722593758418646917333421243995470573738952458096887540672858724327154446205246632810527567209946622345218869420189168275102560733735429956850628043994221546419658990747556229495153544951870939202379746078046060790774432154198394167315112823836578614024385571801798310107052313312758464039710738526298342968814266657491174315805348937886241376366827297266848228004640815768009261685857636900318036250586070516186932441618382927247464293634134278056804241466814178101944562625264752113197961359845934701311035343936502512843348012012662601476991941798753136558125996606029834828060968505181927384404679446403873916062985778347243905959683033262170360674795191209568367131286119138817582876595896526400336461059415906918005678053098735835917461138828452905774940003293335334351257599092806458221771728421785213304793225471366459078596214493106751661839092974195056244710628004137096814475382442973046255268893279010234435230097717103397857957526190849885003232874944343331690911408974885823718484132960678035429435052840576681250060297853833718781388638798865323576531667466248275720915968216859985367785425607674849742044176983649830853427363758909919285908319241775058962827378204160836073089241289054031799984589800618387998452773850294020922605901739784503057950768609818215315239563507671120449866027163372815354750137421089618994947403347786451218778743756335315693367296633806333073829675611100448965726984890396314402567111086515917013165103220979200252852426606057860738160080122794885337940634699655581346746599270379361081434428790635459248729493865106981378690334390144614341027539567090457696571358340283967528576521766919116698763654955150024038513041026333390753761257646974899364886274078134885752484451722948105559885245255652147022764025626275316407391552675567273881795363164334379927317032198614660804001907267184308853903124873889960855917867326218612853024756791807905576861867084396566101749155701106329140571922131171892943930493963812054741148332907761598030283567945864794715700671540983434805768484333752293022278927144769230471419479166670014375939822691447389639631250284675834996740893515191918042377895710075687697540404331374199110453877520823103952313494905252087927533381637410063115535820832, 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'aut_phi_ratio': 9.95, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 199, 2, 1], [3, 1, 1, 2], [6, 1, 1, 2], [6, 199, 2, 2], [9, 199, 3, 2], [11, 199, 1, 10], [18, 199, 3, 2], [18, 199, 6, 2], [22, 199, 1, 10], [22, 199, 2, 10], [33, 199, 1, 20], [66, 199, 1, 20], [66, 199, 2, 20], [99, 199, 3, 20], [198, 199, 3, 20], [198, 199, 6, 20], [199, 66, 3, 1], [398, 66, 3, 1], [597, 66, 3, 2], [1194, 66, 3, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_6\\times F_{199}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 6, 'autcent_group': '6.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 39402, 'autcentquo_group': '39402.d', 'autcentquo_hash': 6821401462869295210, 'autcentquo_nilpotent': False, 'autcentquo_order': 39402, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{199}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 199, 2], [3, 1, 2], [6, 1, 2], [6, 199, 4], [9, 199, 6], [11, 199, 10], [18, 199, 18], [22, 199, 30], [33, 199, 20], [66, 199, 60], [99, 199, 60], [198, 199, 180], [199, 66, 3], [398, 66, 3], [597, 66, 6], [1194, 66, 6]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '13134.h', 'commutator_count': 1, 'commutator_label': '199.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '11.1', '199.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['39402.f', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 199, 1, 2], [3, 1, 2, 1], [6, 1, 2, 1], [6, 199, 2, 2], [9, 199, 6, 1], [11, 199, 10, 1], [18, 199, 6, 3], [22, 199, 10, 3], [33, 199, 20, 1], [66, 199, 20, 3], [99, 199, 60, 1], [198, 199, 60, 3], [199, 66, 3, 1], [398, 66, 3, 1], [597, 66, 6, 1], [1194, 66, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8640, 'exponent': 39402, 'exponents_of_order': [2, 2, 1, 1], 'factors_of_aut_order': [2, 3, 11, 199], 'factors_of_order': [2, 3, 11, 199], 'faithful_reps': [[66, 0, 6]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '26268.a', 'hash': 1173636014134403962, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 13134, 'inner_gen_orders': [66, 199], 'inner_gens': [[1, 13266], [65737, 198]], 'inner_hash': 18, 'inner_nilpotent': False, 'inner_order': 13134, 'inner_split': False, 'inner_tex': 'C_{199}:C_{66}', 'inner_used': [1, 2], 'irrC_degree': 66, 'irrQ_degree': 396, 'irrQ_dim': 396, 'irrR_degree': 132, 'irrep_stats': [[1, 396], [66, 18]], 'label': '78804.b', 'linC_count': 6, 'linC_degree': 66, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 204, 'linQ_degree_count': 6, 'linQ_dim': 204, 'linQ_dim_count': 6, 'linR_count': 594, 'linR_degree': 68, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C398:C198', 'ngens': 6, '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, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 171, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 414, 'number_divisions': 28, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 60, 'number_subgroups': 5208, 'old_label': None, 'order': 78804, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 399], [3, 2], [6, 798], [9, 1194], [11, 1990], [18, 3582], [22, 5970], [33, 3980], [66, 11940], [99, 11940], [198, 35820], [199, 198], [398, 198], [597, 396], [1194, 396]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [3, 6], 'outer_gen_pows': [179, 0], 'outer_gens': [[1, 36234], [39535, 198]], 'outer_group': '18.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 18, 'outer_permdeg': 8, 'outer_perms': [3, 5280], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times C_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 210, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 9, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [6, 4], [10, 4], [20, 4], [60, 4], [198, 2], [396, 2]], 'representations': {'PC': {'code': '781818373271351353049917144153633925076004994710444682774177587108671115697', 'gens': [1, 5], 'pres': [6, -2, -3, -3, -11, -2, -199, 12, 43, 68, 397984, 329680, 101986, 71632, 88, 955157, 791219, 244745, 14279]}, 'GLFp': {'d': 2, 'p': 199, 'gens': [7880799, 1048119676, 1560358800]}, 'Perm': {'d': 210, 'gens': [508744785324364781583041810506704359263093070799993049905934448756445718139588880708401531759089126317550962231488075747826260798838235821783186180212525227794079575973106712168536717645595177741671675705045338991618121528295119002047854895299825053585641297101372437486561826519507026139942245850985371580772032333830790010393277641120957502252995280093121229047240959325372754430038969922355200, 7303501505976875578544969573135445520417819197885419583301895969279290293610490468746023369773048778890943869710126167549306008408019550333549082422000354021596180134576782457416093792137827762927260749565777889729101386141452589228161215626341135125318799401913836008403888725791181226918574854767531788835062205083356900385172123849771031943898956755962098646308286372780101849912675724025110, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 198], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{398}:C_{198}', 'transitive_degree': 3582, '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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [5]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', '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], [3, 1, 2], [6, 1, 2]], 'center_label': '6.2', 'center_order': 6, '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', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 6]], 'label': '6.2', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6', 'ngens': 2, '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': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 6, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[5]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2]], 'representations': {'PC': {'code': 21, 'gens': [1], 'pres': [2, -2, -3, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [73]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 56]}, 'Perm': {'d': 5, 'gens': [24, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}
