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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.6276915', 'ambient_counter': 6276915, 'ambient_order': 512, 'ambient_tex': 'C_2^2\\times C_4^2\\times C_8', 'central': True, 'central_factor': False, 'centralizer_order': 512, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '512.6276915.256.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '256.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '256.53038', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 53038, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_4\\times C_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '512.6276915', 'aut_centralizer_order': None, 'aut_label': '256.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['128.a1', '128.d1', '128.e1', '128.f1'], 'contains': ['512.a1'], 'core': '256.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [64], 'label': '512.6276915.256.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '256.b1', 'normal_contained_in': ['128.a1', '128.d1', '128.e1', '128.f1'], 'normal_contains': ['512.a1'], 'normalizer': '1.a1', 'old_label': '256.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.b1', 'subgroup_fusion': None, 'weyl_group': None}
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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}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '512.6276915', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [12, 8, 12], 'aut_gens': [[1, 8, 32, 128, 256], [473, 432, 424, 340, 144], [487, 30, 376, 384, 336], [329, 458, 176, 404, 128]], 'aut_group': None, 'aut_hash': 8576250844453276636, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2415919104, 'aut_permdeg': 256, 'aut_perms': [619434239630432630340457023031743375430851209793102413780664116286892051240918507853821101435261058445092798119545334429407540069993564146118780525783411243130939119746221843509192592719929312165033789463281483832936342479553847039364490177153292331186623876206051910515513183827685659820354419781431870361556902748688378809481062149412733080988230483602496148887867335236048406799176202871237118393459578136963181065570276328838552448854776928814419760982264068701494940951891151467314951407024786981965226, 199896003246584584875668913910237471189802383069590885643512466139216112236275736009274950106227027928573482670731764065030577913682615871818259227805514040144966071819930510661802564929216672201056829820834183278117638857391998977197313127627649280668655443435992341487720411406222210239598568430037956277498968007085188182834632157300522761904460125089614108661559373255266174251845883069530913251628193171533309143220700938899592632397279327024410497051180436715073480825294219206023761266584995195296791, 651997962795160904201546565840811953859599453141444113630030453258570543551224144967899004556909065484070373118287550184581308337889903686510392112100078916586975197485101553066607521039643582982147040389960409730371248497750565035223748861312762169365393054725218286839970321564202962534216549009403793885679124842120110780185095760656931793341203711845497065249846976306356726908430900408720386693642593029039843278758159404267558833738481178845685296755755165147089174149780011752862735400564191092071821], 'aut_phi_ratio': 9437184.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 1, 24, 1], [4, 1, 8, 1], [4, 1, 24, 1], [4, 1, 192, 1], [8, 1, 256, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^7.C_2^6.C_2.C_2^6.C_2^6.S_3^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': None, 'autcent_hash': 8576250844453276636, 'autcent_nilpotent': False, 'autcent_order': 2415919104, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^7.C_2^6.C_2.C_2^6.C_2^6.S_3^2', '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, 31], [4, 1, 224], [8, 1, 256]], 'center_label': '512.6276915', 'center_order': 512, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, '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': 6276915, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['4.1', 2], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 31], [4, 1, 2, 112], [8, 1, 4, 64]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 4340, 'exponent': 8, 'exponents_of_order': [9], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '32.51', 'hash': 6276915, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1], 'inner_gens': [[1, 8, 32, 128, 256], [1, 8, 32, 128, 256], [1, 8, 32, 128, 256], [1, 8, 32, 128, 256], [1, 8, 32, 128, 256]], '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': None, 'irrep_stats': [[1, 512]], 'label': '512.6276915', 'linC_count': None, 'linC_degree': 5, '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': 'C2^2*C4^2*C8', 'ngens': 5, 'nilpotency_class': 1, '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 512, 'number_divisions': 208, 'number_normal_subgroups': 6594, 'number_subgroup_autclasses': 84, 'number_subgroup_classes': 6594, 'number_subgroups': 6594, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 31], [4, 224], [8, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [12, 4, 8], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[293, 136, 490, 452, 196], [329, 88, 162, 128, 388], [95, 290, 152, 336, 212]], 'outer_group': None, 'outer_hash': 8576250844453276636, 'outer_nilpotent': False, 'outer_order': 2415919104, 'outer_permdeg': 256, 'outer_perms': [475831663372236567638326585736311422259782290211951082468940904718633999584575967616207856663079989212762211781066755577466882503739518220140235483684316635441001880706030745158869706408857712884849769073783549165143345914809152151015967351528912994614527549448307957579738430325854981530500704008623502953084483436666313170907862390892212814480953354332685167436780679796432050315382761660016362004108015256086702864568833562873086943289405392218923253300826770560471597122066641679066212084880237854572937, 561525649011323333915784928942064335359154615167887308067926621443781157947642017436418777226819740599395497033240585831493367764537296323485901429913848508292388165586126560084465840308615179120396831807786675624600853394727457560412561742562800552534939116922820046143565855053570618811560613196830212847699608287219148853672513744844647807540441865252379235179319131251822217711108289840568712966815797304876001323261061925498477980755922696341769388440478620947177285287115529369024902892566280778938301, 42905107585067620543146078105692004453682817586644128236722353955444205172502572226649942752411534218704110731074276222264337278911302173748199557728190582372303352994149897157128254422541275344897305359761435317464850511540013298935314088970953428114114938924749396772064727872889707201333406485247934021358984284006199239272396122367611700902277734322886961554516583779987046117043073904947832560377446916548391724269125504143255311476695772914237317916992166667014464981017465512203116106419924880216568], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^7.C_2^6.C_2.C_2^6.C_2^6.S_3^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4, 4, 8], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 112], [4, 64]], 'representations': {'PC': {'code': '9519098654586245742635', 'gens': [1, 4, 6, 8, 9], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 46, 102, 158]}, 'Perm': {'d': 20, 'gens': [40176, 4097379686400, 127008000, 355687428096000, 121645100408832000, 16582, 1313901388800, 40279680, 5167]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 4, 4, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4, 4, 8], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_4^2\\times C_8', 'transitive_degree': 512, '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': '256.53038', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 168, 'aut_gen_orders': [28, 12, 24], 'aut_gens': [[1, 2, 4, 8, 32], [132, 145, 22, 91, 105], [3, 151, 145, 11, 232], [17, 23, 130, 220, 236]], 'aut_group': None, 'aut_hash': 5302274406425492967, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 88080384, 'aut_permdeg': 128, 'aut_perms': [126103313064787726297673456756029641913976405645893512836830131611665225364159985861987983552317302532149244643009907824666744676311697700611182673569400029997406626781853373686128909913315545741060623219287584510979, 315843097489821333113988489494114294144521031474269653761040257182033755087624910429737741122596382369476657442079695082199563467738095223944868483933751874748833133234155699347429977535285886545983409360161158026118, 328331905692079261377285010693327746891749928996802904345869226609532956205629063555521669662717194430043208552919329273140780600241089275654978697351636332732996474814969449330613621759740535897333583007449330226123], 'aut_phi_ratio': 688128.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 1, 28, 1], [4, 1, 4, 1], [4, 1, 28, 1], [4, 1, 64, 1], [8, 1, 128, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.C_2^5.C_2^6.C_2^2.\\PSL(2,7)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 168, 'autcent_group': None, 'autcent_hash': 5302274406425492967, 'autcent_nilpotent': False, 'autcent_order': 88080384, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^6.C_2^5.C_2^6.C_2^2.\\PSL(2,7)', '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, 31], [4, 1, 96], [8, 1, 128]], 'center_label': '256.53038', 'center_order': 256, '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', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 53038, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 3], ['4.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 31], [4, 1, 2, 48], [8, 1, 4, 32]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3720, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '32.51', 'hash': 53038, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8, 32], [1, 2, 4, 8, 32], [1, 2, 4, 8, 32], [1, 2, 4, 8, 32], [1, 2, 4, 8, 32]], '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, 256]], 'label': '256.53038', 'linC_count': None, 'linC_degree': 5, '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': 'C2^3*C4*C8', 'ngens': 5, 'nilpotency_class': 1, '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 256, 'number_divisions': 112, 'number_normal_subgroups': 2319, 'number_subgroup_autclasses': 57, 'number_subgroup_classes': 2319, 'number_subgroups': 2319, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 31], [4, 96], [8, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 168, 'outer_gen_orders': [4, 12, 4], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[145, 7, 132, 156, 41], [3, 20, 22, 218, 248], [129, 19, 5, 159, 227]], 'outer_group': None, 'outer_hash': 5302274406425492967, 'outer_nilpotent': False, 'outer_order': 88080384, 'outer_permdeg': 128, 'outer_perms': [29180317846392730731093894385882836941262401930341658036602928573050217665124743362914024937616708969923314238752498748025280256969264786332907035958949965725739538066743386754338229435299646818868625844388447784189, 364433753495042476832227503163485376141778740587285301167239343630879093471953620963098526586594152430625816779517969064956146975037557603853537238583587230805040307040170791171624258992828510255429887308488135443384, 299080663679963708406565722778251330040136564392635872246263202292287305185709798342175570857748475901400060930719230985708780384987627944437384569582422716378543999547845425114728746542408766396592721463021183669461], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2^6.C_2^5.C_2^6.C_2^2.\\PSL(2,7)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 18, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 4, 8], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 48], [4, 32]], 'representations': {'PC': {'code': 2269666877636712, 'gens': [1, 2, 3, 4, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 91, 141, 166]}, 'GLZN': {'d': 2, 'p': 24, 'gens': [13969, 18641, 76325, 158987, 186925, 136429, 76337, 14113]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [4105, 39041, 36873, 13359, 4161, 22669, 12291, 4225]}, 'Perm': {'d': 18, 'gens': [40176, 127008000, 6227020800, 355687428096000, 1307674368000, 16582, 40279680, 5167]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4, 8], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3\\times C_4\\times C_8', 'transitive_degree': 256, 'wreath_data': None, 'wreath_product': False}
