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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '10616832.ko', 'ambient_counter': 275, 'ambient_order': 10616832, 'ambient_tex': 'D_4^3.A_4^3:A_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '10616832.ko.663552._.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '663552.C', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '663552.jo', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 663552, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5.A_4^3:A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': None, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '10616832.ko', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [8691540457481575679470548815548473721, 40284847, 10341839515696277368485150895177728000000, 25903229683158464681647], 'label': '10616832.ko.663552._.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '663552.C', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '663552._.C', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 420, 'aut_gen_orders': [6, 3], 'aut_gens': [[1, 2, 4, 8], [12, 4, 5, 3], [10, 14, 7, 5]], 'aut_group': '20160.a', 'aut_hash': 3764836782182912467, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20160, 'aut_permdeg': 8, 'aut_perms': [5193, 5760], 'aut_phi_ratio': 2520.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 15, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_8', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 420, 'autcent_group': '20160.a', 'autcent_hash': 3764836782182912467, 'autcent_nilpotent': False, 'autcent_order': 20160, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'A_8', '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, 15]], 'center_label': '16.14', 'center_order': 16, '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'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 14, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 4]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [4], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '16.14', 'hash': 14, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8]], '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, 16]], 'label': '16.14', 'linC_count': 840, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 840, 'linQ_dim': 4, 'linQ_dim_count': 840, 'linR_count': 840, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^4', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 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': 16, 'number_divisions': 16, 'number_normal_subgroups': 67, 'number_subgroup_autclasses': 5, 'number_subgroup_classes': 67, 'number_subgroups': 67, 'old_label': None, 'order': 16, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 15]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 420, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[12, 4, 5, 3], [10, 14, 7, 5]], 'outer_group': '20160.a', 'outer_hash': 3764836782182912467, 'outer_nilpotent': False, 'outer_order': 20160, 'outer_permdeg': 8, 'outer_perms': [5193, 5760], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'A_8', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3, 4], 'pres': [4, -2, 2, 2, 2]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [7233746, 7115648, 35812976, 7115160]}, 'GLFp': {'d': 4, 'p': 2, 'gens': [33837, 18465, 27183, 18467]}, 'Perm': {'d': 8, 'gens': [5040, 120, 6, 1]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4', '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': '12.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[63806087362571409346165044965962442915152, 276552843805858172455956208056563250489727, 201787255109196483509209667445320361558456, 137989910791554027252411880721143668314753], [63806087362571409346165044965962483199999, 276552843805858172455956208056563210940720, 201787255109196483483306437762174431487863, 127648087721556836004576187662983492529358], [63806087362571409346165044965962483199999, 286894666858193586458696232929555978940720, 191462782246443131640095793552353961558456, 127648087721556835978673201981413196030158], [31598626812650889910023018345982008906832, 276552843805858172455956208056563250489727, 170197396577071941302662020485122066026833, 212746663229648355057587258688425032147320], [63806087362571409346165044965962483199999, 276561518900638314627466726811737915836720, 201795930203976625680669094900026847119937, 127656762816337009224358931462807876897272], [63806087362571409238098484005414477614023, 308187197206674165501289770643102150790520, 148913473390917152929817942474054761339560, 170197396577082814606736009101304083753553], [63806087362571409346165044965962707419496, 276561518900649218979761849176017797897527, 159246621348450647104412638746942011241473, 223088494513664216092390145327541195688176], [63806087362571409238098484005414213119999, 297845374154349624911007598492828396611241, 191454107151662989254596960077183255105792, 223088528502616873380399418942730573814961], [63806087362571409238098484005414172835152, 329443975713742149436630923119056381347120, 170206037691741203636947503492970435838136, 234012133313760421625921314178444674329742], [63806087362571409238098484005414477614023, 297845374154360498186981946653136702331456, 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[95431807898082064705247944385104864016056, 286894675089874002766577193650169499415742, 244345273057307927971090370684491875278777, 180539193880965987207423307846374892819177], [63806087362571409346165044965962442920319, 286894666858182713100455857908381194940727, 201787255109196483509209545443231117567856, 137989910791554027278314866401412477182153], [74147926878256782308188686380492314787152, 276552843805858172430052978374718687932727, 191462782246432258255952188849334654550456, 137989910791554027252411880721143628035078], [63806087362571409346165044965962442915152, 276552835574188629642534063397631538494640, 201787255109196483483306559762962228136183, 137989910791554027252411758721657278729038], [63806087362571409346165044965962442915152, 286894675089874002604455522927817991486640, 191462782246432258255952310848821084415856, 127648087721545962620432704960752062733953], [63806087362571409346164922966476053339519, 286894675089874002604455644929919690249527, 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[63806087362571409238098484005414477614023, 286894666858182713074552628226536671932727, 191462782246443131506074778230805144406392, 212755380527378077533325170305717740814022], [63806087362571409238098484005414477614023, 286894666858182713074552628226536671932727, 191462782246443131531977763912375401346519, 212755380527378077533325170305717740814022], [74147926878245877845262711534298661339496, 286894666858182713074552628226536671932727, 191462782246443131506074778230805144406392, 212755380527378077559228155987288076872297], [95431790885335019639220531161514533052119, 201795938435667946124925002317763171191086, 350727873718592252830077478461050375558400, 319102144429726319100107601146217608892216], [10341890472001896255177345564137892350032, 286894666858193586432793003249025357321520, 180539219647090879292881449267201939035376, 223079811187203626863015717721430709155127]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 8153726976, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 8, 1], [2, 8, 2, 1], [2, 9, 1, 2], [2, 9, 3, 2], [2, 12, 4, 2], [2, 18, 24, 1], [2, 24, 2, 1], [2, 27, 1, 4], [2, 27, 3, 2], [2, 36, 12, 2], [2, 54, 24, 1], [2, 72, 2, 1], [2, 72, 6, 1], [2, 81, 1, 2], [2, 108, 4, 2], [2, 108, 12, 2], [2, 162, 8, 1], [2, 216, 2, 2], [2, 216, 6, 1], [2, 216, 24, 1], [2, 324, 4, 4], [2, 432, 12, 2], [2, 648, 2, 1], [2, 648, 24, 1], [2, 864, 2, 1], [2, 864, 6, 1], [2, 1296, 12, 2], [2, 2592, 2, 1], [2, 2592, 6, 1], [3, 24, 1, 1], [3, 192, 1, 1], [3, 256, 2, 1], [3, 36864, 2, 1], [4, 6, 4, 1], [4, 8, 1, 1], [4, 12, 2, 1], [4, 12, 8, 1], [4, 18, 12, 1], [4, 24, 2, 3], [4, 36, 6, 1], [4, 36, 24, 1], [4, 54, 12, 1], [4, 72, 1, 1], [4, 72, 6, 3], [4, 108, 4, 2], [4, 108, 6, 1], [4, 108, 8, 2], [4, 108, 24, 1], [4, 162, 4, 1], [4, 216, 1, 2], [4, 216, 6, 3], [4, 216, 12, 2], [4, 216, 24, 2], [4, 216, 48, 1], [4, 324, 2, 1], [4, 324, 4, 2], [4, 324, 8, 3], [4, 432, 6, 2], [4, 432, 12, 3], [4, 432, 24, 6], [4, 648, 2, 3], [4, 648, 12, 2], [4, 648, 24, 2], [4, 648, 48, 1], [4, 864, 1, 2], [4, 864, 2, 2], [4, 864, 4, 1], [4, 864, 6, 7], [4, 864, 12, 4], [4, 1296, 6, 2], [4, 1296, 12, 3], [4, 1296, 24, 6], [4, 2592, 1, 2], [4, 2592, 2, 2], [4, 2592, 4, 1], [4, 2592, 6, 7], [4, 2592, 12, 4], [6, 24, 1, 1], [6, 24, 3, 2], [6, 48, 24, 1], [6, 72, 2, 2], [6, 72, 6, 2], [6, 96, 12, 2], [6, 144, 48, 1], [6, 192, 1, 1], [6, 192, 2, 1], [6, 192, 3, 2], [6, 192, 6, 1], [6, 216, 1, 2], [6, 216, 3, 2], [6, 256, 2, 1], [6, 288, 24, 2], [6, 384, 24, 1], [6, 432, 24, 1], [6, 576, 1, 2], [6, 576, 3, 2], [6, 576, 4, 1], [6, 576, 12, 1], [6, 768, 2, 2], [6, 768, 12, 2], [6, 864, 4, 2], [6, 864, 12, 2], [6, 1152, 24, 1], [6, 1536, 2, 1], [6, 1536, 6, 1], [6, 1536, 16, 1], [6, 1728, 2, 1], [6, 1728, 6, 1], [6, 1728, 24, 1], [6, 2048, 4, 1], [6, 2304, 12, 2], [6, 3072, 8, 2], [6, 3456, 12, 2], [6, 4608, 2, 1], [6, 4608, 6, 1], [6, 6144, 4, 1], [6, 6912, 2, 1], [6, 6912, 6, 1], [6, 36864, 2, 1], [6, 73728, 4, 1], [6, 110592, 2, 2], [6, 221184, 4, 1], [9, 147456, 4, 1], [12, 48, 12, 1], [12, 96, 6, 1], [12, 96, 24, 1], [12, 144, 24, 1], [12, 192, 1, 1], [12, 192, 6, 3], [12, 288, 12, 1], [12, 288, 24, 2], [12, 384, 12, 1], [12, 432, 12, 1], [12, 576, 2, 1], [12, 576, 12, 3], [12, 768, 6, 1], [12, 768, 24, 1], [12, 864, 4, 2], [12, 864, 6, 1], [12, 864, 8, 2], [12, 864, 24, 1], [12, 1152, 12, 1], [12, 1536, 1, 1], [12, 1536, 6, 3], [12, 1536, 8, 1], [12, 1728, 1, 1], [12, 1728, 6, 3], [12, 1728, 12, 2], [12, 1728, 24, 2], [12, 1728, 48, 1], [12, 2048, 2, 1], [12, 2304, 6, 1], [12, 2304, 24, 1], [12, 3072, 4, 1], [12, 3072, 16, 1], [12, 3456, 6, 2], [12, 3456, 12, 3], [12, 3456, 24, 6], [12, 4608, 1, 1], [12, 4608, 6, 3], [12, 6144, 4, 3], [12, 6912, 1, 2], [12, 6912, 2, 2], [12, 6912, 4, 1], [12, 6912, 6, 7], [12, 6912, 12, 4], [12, 73728, 2, 1], [12, 221184, 2, 1], [18, 147456, 4, 1], [18, 294912, 8, 1], [36, 294912, 4, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 6, 8], [2, 8, 2], [2, 9, 8], [2, 12, 8], [2, 18, 24], [2, 24, 2], [2, 27, 10], [2, 36, 24], [2, 54, 24], [2, 72, 8], [2, 81, 2], [2, 108, 32], [2, 162, 8], [2, 216, 34], [2, 324, 16], [2, 432, 24], [2, 648, 26], [2, 864, 8], [2, 1296, 24], [2, 2592, 8], [3, 24, 1], [3, 192, 1], [3, 256, 2], [3, 36864, 2], [4, 6, 4], [4, 8, 1], [4, 12, 10], [4, 18, 12], [4, 24, 6], [4, 36, 30], [4, 54, 12], [4, 72, 19], [4, 108, 54], [4, 162, 4], [4, 216, 140], [4, 324, 34], [4, 432, 192], [4, 648, 126], [4, 864, 100], [4, 1296, 192], [4, 2592, 100], [6, 24, 7], [6, 48, 24], [6, 72, 16], [6, 96, 24], [6, 144, 48], [6, 192, 15], [6, 216, 8], [6, 256, 2], [6, 288, 48], [6, 384, 24], [6, 432, 24], [6, 576, 24], [6, 768, 28], [6, 864, 32], [6, 1152, 24], [6, 1536, 24], [6, 1728, 32], [6, 2048, 4], [6, 2304, 24], [6, 3072, 16], [6, 3456, 24], [6, 4608, 8], [6, 6144, 4], [6, 6912, 8], [6, 36864, 2], [6, 73728, 4], [6, 110592, 4], [6, 221184, 4], [9, 147456, 4], [12, 48, 12], [12, 96, 30], [12, 144, 24], [12, 192, 19], [12, 288, 60], [12, 384, 12], [12, 432, 12], [12, 576, 38], [12, 768, 30], [12, 864, 54], [12, 1152, 12], [12, 1536, 27], [12, 1728, 139], [12, 2048, 2], [12, 2304, 30], [12, 3072, 20], [12, 3456, 192], [12, 4608, 19], [12, 6144, 12], [12, 6912, 100], [12, 73728, 2], [12, 221184, 2], [18, 147456, 4], [18, 294912, 8], [36, 294912, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': None, 'commutator_count': 2, 'commutator_label': None, 'complements_known': False, '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', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 21, 'conjugacy_classes_known': False, 'counter': 275, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 8], [2, 8, 1, 2], [2, 9, 1, 8], [2, 12, 1, 8], [2, 18, 1, 24], [2, 24, 1, 2], [2, 27, 1, 10], [2, 36, 1, 24], [2, 54, 1, 24], [2, 72, 1, 8], [2, 81, 1, 2], [2, 108, 1, 32], [2, 162, 1, 8], [2, 216, 1, 34], [2, 324, 1, 16], [2, 432, 1, 24], [2, 648, 1, 26], [2, 864, 1, 8], [2, 1296, 1, 24], [2, 2592, 1, 8], [3, 24, 1, 1], [3, 192, 1, 1], [3, 256, 2, 1], [3, 36864, 2, 1], [4, 6, 1, 4], [4, 8, 1, 1], [4, 12, 1, 10], [4, 18, 1, 12], [4, 24, 1, 6], [4, 36, 1, 30], [4, 54, 1, 12], [4, 72, 1, 19], [4, 108, 1, 54], [4, 162, 1, 4], [4, 216, 1, 140], [4, 324, 1, 34], [4, 432, 1, 192], [4, 648, 1, 126], [4, 864, 1, 100], [4, 1296, 1, 192], [4, 2592, 1, 100], [6, 24, 1, 7], [6, 48, 1, 24], [6, 72, 1, 16], [6, 96, 1, 24], [6, 144, 1, 48], [6, 192, 1, 15], [6, 216, 1, 8], [6, 256, 2, 1], [6, 288, 1, 48], [6, 384, 1, 24], [6, 432, 1, 24], [6, 576, 1, 24], [6, 768, 1, 24], [6, 768, 2, 2], [6, 864, 1, 32], [6, 1152, 1, 24], [6, 1536, 1, 8], [6, 1536, 2, 8], [6, 1728, 1, 32], [6, 2048, 2, 2], [6, 2304, 1, 24], [6, 3072, 2, 8], [6, 3456, 1, 24], [6, 4608, 1, 8], [6, 6144, 2, 2], [6, 6912, 1, 8], [6, 36864, 2, 1], [6, 73728, 2, 2], [6, 110592, 2, 2], [6, 221184, 2, 2], [9, 147456, 2, 2], [12, 48, 1, 12], [12, 96, 1, 30], [12, 144, 1, 24], [12, 192, 1, 19], [12, 288, 1, 60], [12, 384, 1, 12], [12, 432, 1, 12], [12, 576, 1, 38], [12, 768, 1, 30], [12, 864, 1, 54], [12, 1152, 1, 12], [12, 1536, 1, 19], [12, 1536, 2, 4], [12, 1728, 1, 139], [12, 2048, 2, 1], [12, 2304, 1, 30], [12, 3072, 2, 10], [12, 3456, 1, 192], [12, 4608, 1, 19], [12, 6144, 2, 6], [12, 6912, 1, 100], [12, 73728, 2, 1], [12, 221184, 2, 1], [18, 147456, 2, 2], [18, 294912, 2, 4], [36, 294912, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [17, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 1, 192], [36, 1, 192], [54, 1, 192], [72, 1, 48], [108, 1, 96], [162, 1, 64]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '1327104.lb', 'hash': 2102089609429699307, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 5308416, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': 18, 'irrQ_degree': 18, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 12], [3, 84], [4, 24], [6, 192], [8, 3], [9, 256], [12, 216], [18, 448], [24, 105], [27, 268], [32, 6], [36, 304], [48, 22], [54, 320], [72, 100], [81, 84], [96, 1], [108, 144], [144, 16], [162, 64], [216, 31], [288, 1], [324, 16], [432, 2], [648, 1]], 'label': '10616832.ko', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'D4^3.A4^3:A4', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 0, 1, 0, 1, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 16, 0, 0, 0, 0, 7, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 1, 6, 0, 0, 0, 1, 15, 0, 0, 0, 5, 6, 0, 0, 0, 5, 3, 0, 0, 0, 4, 1, 0, 0, 0, 22, 0, 0, 0, 0, 63, 0, 0, 0, 0, 42, 0, 0, 0, 63, 0, 0, 22, 0, 0, 3, 1, 1, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 302, 'number_characteristic_subgroups': 49, 'number_conjugacy_classes': 2720, 'number_divisions': 2655, 'number_normal_subgroups': 313, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 10616832, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 107135], [3, 74456], [4, 810368], [6, 2241064], [9, 589824], [12, 2665216], [18, 2949120], [36, 1179648]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '1536.408626275', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 1536, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^4:\\GL(2,\\mathbb{Z}/4)', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 4], [3, 84], [6, 192], [8, 13], [9, 256], [12, 176], [16, 1], [18, 448], [24, 93], [27, 260], [36, 304], [48, 30], [54, 324], [64, 3], [72, 100], [81, 84], [96, 5], [108, 144], [144, 16], [162, 64], [216, 29], [288, 1], [324, 16], [432, 3], [648, 1]], 'representations': {'PC': {'code': '272867640067397484356981951879358257631545105791114289268785580705194544357538583873298764457565616228711364846897138265641912789686056265975737594128402634118012751432173754455761843094515856613650974508838621932260596023979242532130034218591586236690050798266120843182994370818240410379449909590728587480672491163156729168489817037989485668083291167061063965038636459591933164622625834047595767664156116323763477803305336881751841882257985906940434075307419022498432103616449826463211884675042144868504826103372175086725568277738379747027590008050234199777075996051761123900015413027062874580412658372605028229873650243189816333476474895261321868827420234740723915740264668922265726551697318988621840712603268889526043433684999180691984754210392179440933672921826109717187762819891925992472561553456234037808784332175785277489384089931839544102053166333548141694849793995036758427903042510102224587984744818857577248516134623925244735735456598353947556265412608', 'gens': [1, 3, 4, 6, 8, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21], 'pres': [21, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 42, 17908150, 440651990, 99565034, 217772, 536680875, 338876772, 885, 234, 747290884, 54522745, 363766, 90808, 56234309, 644852906, 20564759, 8740184, 362, 18419694, 571687731, 13808640, 257613, 21300, 95840647, 640507420, 81297265, 40382566, 1164331, 1507072, 7983997, 490, 678503960, 51288581, 9539279, 383405, 790532, 554, 610187769, 15452670, 2600712, 1759074, 788895, 338943538, 264972739, 997972, 499033, 2744395, 941564747, 975884144, 3701450, 29093999, 3157172, 12211049, 18302, 1733, 746, 707628, 113218593, 177557197, 97542178, 342413623, 171206860, 28619254, 14267371, 941401454, 1123476515, 373403576, 181258637, 29846999, 15105020, 453761, 189182, 113603, 20901903, 101025828, 154586937, 81938382, 38646819, 1147426576, 1354703653, 570166186, 280147975, 48464992, 33620953, 17992942, 222931, 197248, 55897, 15676433, 114143942, 226165019, 107857088, 56541341, 403341138, 442425603, 143410236, 84115665, 67956186, 10801851, 15283440, 1723845, 890754, 431127, 166212, 83241, 4276177939, 1580705320, 508213501, 235237042, 49351783, 55762684, 27639505, 3104806, 1582747, 776368, 1579725524, 1800671837, 641834990, 340730795, 100590440, 35816381, 16701698, 5567351, 2984876, 1392005, 522374, 261323]}, 'Perm': {'d': 36, 'gens': [137989910791554027252411880721143668314753, 276552843805858172455956208056563250489727, 201787255109196483509209667445320361558456, 63806087362571409346165044965962442915152]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 9, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'D_4^3.A_4^3:A_4', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[106364087758554854040895081254934497643583, 223088502736491981346645323448727276755216, 42558000396016933369061830957812444916422, 276552877794833413983470832754237785790201], [106364087758554854040895081254934497643583, 223088502736491981346645323448727276755216, 42558000396016933369061830957812444916422, 276552877794833413983470832754237785790201], [31598652011695140852934618286797943805481, 201795981177964977212725901154596324630543, 10341831284004957086402395688242700041673, 340403366318675237619628539735333100569726], [106364087758554854040895081254934497643583, 212746663220817481717061009257871045206463, 42558000396016933369061830957812444916422, 286894700847168827960410053121231714673401], 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42558000396016933369061830957812309002903, 297845365931544443842040793493414456437096], [116688544193325294899883098627037153643583, 191454149893949116015903269939525092630543, 21256820727690183928603192922229468916422, 297845374145530431807685373684421785431801], [106364087758554853904624915439874332174598, 137981176508822114393701878048046214723257, 42558000396016933369061708958338373463703, 297845365931544444086377519915944185251193], [106364079544547057476051503800768481643583, 212746671452497897862922725142052150483216, 52882456830787374228049848329915140470337, 276552877794833413957669906958825925662641], [106364087758554854040895081254934497643583, 223088502736491981320844519652801806934456, 42558000396016933369061830957812484470337, 286894709078849244157873377307337009515441], [106364087758554854040895081254934537918103, 223088502736491981346645445450816561035583, 42558000396016933369061830957812484470337, 276552869563163871170048688095306073795126], 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31598618022753388107605807383967316693822, 350727822753456551836856932128610580854321], [42220633073647645235957275271952006, 201795981177964977212725901154596324630543, 31598618022753388107605807383967316693822, 350727822753456551916610148950807587318982], [63814795924662835360433624813557864279703, 127656711860065654708771119926099214934456, 21256812496020672163504120605538309211398, 276552877794833414119689529885589257227006], [106364087758554853904624915439874636585537, 340403366318686111273909039669756031760001, 52882456830776470117629490802298333194887, 127656762825167882402763254431762056475456]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 3822059520, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 17280.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 5, 2], [2, 9, 1, 2], [2, 9, 15, 2], [2, 27, 1, 4], [2, 27, 15, 2], [2, 81, 5, 2], [2, 108, 16, 2], [2, 324, 16, 2], [3, 24, 1, 1], [3, 192, 1, 1], [3, 256, 2, 1], [3, 9216, 2, 1], [4, 108, 16, 2], [4, 108, 32, 2], [4, 324, 16, 2], [4, 324, 32, 2], [6, 24, 1, 1], [6, 24, 15, 2], [6, 72, 2, 2], [6, 72, 30, 2], [6, 192, 1, 1], [6, 192, 15, 2], [6, 216, 1, 2], [6, 216, 15, 2], [6, 256, 2, 1], [6, 576, 1, 2], [6, 576, 15, 2], [6, 768, 10, 2], [6, 864, 16, 2], [6, 9216, 2, 1], [6, 27648, 2, 2], [9, 36864, 4, 1], [12, 864, 16, 2], [12, 864, 32, 2], [18, 36864, 4, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 10], [2, 9, 32], [2, 27, 34], [2, 81, 10], [2, 108, 32], [2, 324, 32], [3, 24, 1], [3, 192, 1], [3, 256, 2], [3, 9216, 2], [4, 108, 96], [4, 324, 96], [6, 24, 31], [6, 72, 64], [6, 192, 31], [6, 216, 32], [6, 256, 2], [6, 576, 32], [6, 768, 20], [6, 864, 32], [6, 9216, 2], [6, 27648, 4], [9, 36864, 4], [12, 864, 96], [18, 36864, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '331776.gg', 'commutator_count': 2, 'commutator_label': None, 'complements_known': False, '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', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 17, 'conjugacy_classes_known': False, 'counter': 249, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['331776.gg', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 10], [2, 9, 1, 32], [2, 27, 1, 34], [2, 81, 1, 10], [2, 108, 1, 32], [2, 324, 1, 32], [3, 24, 1, 1], [3, 192, 1, 1], [3, 256, 2, 1], [3, 9216, 2, 1], [4, 108, 1, 96], [4, 324, 1, 96], [6, 24, 1, 31], [6, 72, 1, 64], [6, 192, 1, 31], [6, 216, 1, 32], [6, 256, 2, 1], [6, 576, 1, 32], [6, 768, 2, 10], [6, 864, 1, 32], [6, 9216, 2, 1], [6, 27648, 2, 2], [9, 36864, 2, 2], [12, 864, 1, 96], [18, 36864, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [13, 4], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '663552.jo', 'hash': 6616857129994665661, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [12, 9, 4, 9], 'inner_gens': [[106364087758554854040895081254934497643583, 244345290033468371655397763079270361118153, 95431824874254219110947900657453524059398, 361660136611701160727088548324698346337223], [85107360225497759642304698417055690721897, 223088502736491981346645323448727276755216, 21256812496020672407841239080799668920360, 286894700847157954764188921784428354647822], [74139260573419295261652182461634440969673, 148913515593866702564029441446382443547456, 42558000396016933369061830957812444916422, 276552877794833414091640088582603866574641], [85107351993817343362523878688043976385158, 201795955411850958539776581046095705388662, 8231680416251518297991613869812422, 276552877794833413983470832754237785790201]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 331776, 'inner_split': None, 'inner_tex': 'C_2^4.A_4^3:A_4', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 6], [3, 42], [4, 12], [6, 64], [9, 128], [12, 52], [18, 128], [27, 134], [36, 32], [54, 64], [81, 42]], 'label': '663552.jo', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C2^5.A4^3:A4', '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, 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, 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': 64, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 704, 'number_divisions': 684, 'number_normal_subgroups': 118, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 663552, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 15871], [3, 19160], [4, 41472], [6, 209192], [9, 147456], [12, 82944], [18, 147456]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '20000.ey', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 11520, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_5^3:C_{20}.Q_8', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 2], [3, 42], [6, 64], [8, 6], [9, 128], [12, 32], [18, 128], [24, 10], [27, 130], [36, 32], [54, 66], [81, 42]], 'representations': {'PC': {'code': '4990169134448801261162736196645265778809485730607535028982380979297425175411647922870726514190555972295553547544113498712223172428965052932331032041970835871063339632721702062503041158037714891028671049267464099143949127539019887509723535492185190146012292830105810515943824317108909232917351264324546731441568838369565497666609639883745201994408726550048068482729721664539985755740699020125114406890186365583051481712965164514070286502145616900242439625684757064659046922241346898289760138132126212365683733593065681909107601864253131634625319671969750643214316369028298784116741376', 'gens': [1, 3, 4, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17], 'pres': [17, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 34, 8443986, 5485664, 10930645, 1189764, 16516251, 9434408, 353229, 190, 35226724, 6517821, 6977518, 1670832, 15184949, 3740566, 809103, 608996, 347383, 294, 42157422, 2837459, 962512, 4681041, 2127794, 41599687, 41753112, 3221609, 5077210, 590043, 715724, 92317, 398, 4766264, 10861801, 1233834, 1806683, 303016, 299361, 50600, 94296969, 45055466, 330540, 238757, 3154, 393321, 120004642, 22316607, 484748, 5735725, 121254, 885353, 437692, 68475467, 9517852, 528830, 176335, 73322508, 15466493, 1145710, 191007, 286496, 150265597, 68346966, 3495791, 8739424, 514161, 1555190, 711259, 54396, 37277, 90882014, 54198751, 2423568, 1652465, 1211842, 202059, 229616, 76633, 16980, 89538063, 13042976, 13865521, 14923074, 2232659, 2423620, 1028277, 133958, 96439, 40450768, 4494561, 1347419, 7921]}, 'Perm': {'d': 36, 'gens': [42558000396016933369061830957812444916422, 276552877794833413983470832754237785790201, 106364087758554854040895081254934497643583, 223088502736491981346645323448727276755216]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 9, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5.A_4^3:A_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
