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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.12235', 'ambient_counter': 12235, 'ambient_order': 1728, 'ambient_tex': '(C_4\\times \\He_3).\\SD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 1, 'counter': 127, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1728.12235.1728.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1728.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1728.12235', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12235, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1728, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_4\\times \\He_3).\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D4', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
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{'ambient': '1728.12235', 'aut_centralizer_order': None, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['576.a1.a1', '576.b1.a1', '864.a1.a1', '864.b1.a1', '864.c1.a1'], 'contains': [], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5036, 7557, 4082, 3406, 3677, 7474, 3742, 3815], 'generators': [], 'label': '1728.12235.1728.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1728.a1.a1', 'normal_contained_in': ['576.a1.a1', '864.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1728.a1.a1', 'projective_image': '1728.12235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', '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': [], '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]], '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [12, 6, 12, 6, 8], 'aut_gens': [[1, 2, 16, 48, 144], [821, 710, 624, 608, 1008], [17, 486, 592, 704, 720], [1013, 150, 1248, 1168, 1008], [409, 1318, 688, 1248, 720], [773, 130, 1248, 1232, 1584]], 'aut_group': None, 'aut_hash': 2187308893640632527, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3456, 'aut_permdeg': 216, 'aut_perms': [5603060225526383134142276303093553422263230392186004662371031927011874072850863872447265703874416717487391363104214624332833032224073943075174376788745043411438477193674259249548728794691815000740400140511421542244318766072353647496489458182717602886110448869663277691753518055977790179823348819218028136749622511764142913023872700380173165716519281927356228415877362596993313726742883382107986411605301551796987, 9681315748443027962480390452081246070822147096765362667631119335722466526578018110238149495427532721876757951575059131723733255908149571672877428959963763688281239726303998723032145880258535167017425892216603562125040785874121671479871754196665329640982489006292014851471421690361022668558150157814422325268895699327077635385261142595662610054277475118773678721130531057424745713723064287862578405939943821468389, 831465534153733344948450210965887118143027200781097621931530464350196709871430780648566044493555724959951753325285386127278492558016962244142375992357103931874756583233320778037960646215530565514450051083215021381671027733597356658073346275881284146072578350122178588143891407782166998841717742598547902513952387299860393043237075577122201550825103335582121003211215171573648303225681687797554910189500210638547, 9239183502231379490779248497500063826335330193922907139291086419163926701263599569243845430306475519315716203036003010188606357134993443911643775802316682186671349940274527953328479422844199105413606230594077076707028186636984908940233878757628707481576724577466156669363702652035719630722268017110494830847430549624711242902874554098426597808580752659304195262094179363057931372341835361308392105258993332765735, 7673126080584001373759184784099883657677504954874445072423081863796230720343513486821279855674867601936573770266450879042716269413222415276056110641634529297361565407368519315808312674600736986342745608639270469495387900161469301530807695232011121553440518214461524780845172757915499374698916076436101373450978577613103081084957390366980239325245432020723951306467739207320313314584739600201823408026001368213167], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 1], [2, 72, 1, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [4, 72, 1, 1], [4, 72, 2, 1], [6, 2, 1, 1], [6, 18, 1, 2], [6, 24, 1, 1], [6, 72, 2, 1], [8, 18, 1, 2], [8, 36, 1, 1], [12, 4, 1, 1], [12, 24, 1, 2], [12, 36, 1, 1], [12, 72, 2, 3], [16, 108, 2, 2], [24, 36, 1, 4]], 'aut_supersolvable': False, 'aut_tex': '\\He_3.(C_2\\times C_4\\times D_4).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '864.3997', 'autcentquo_hash': 3997, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SU(3,2):C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 18, 1], [2, 72, 1], [3, 2, 1], [3, 24, 1], [4, 2, 1], [4, 18, 1], [4, 72, 3], [6, 2, 1], [6, 18, 2], [6, 24, 1], [6, 72, 2], [8, 18, 2], [8, 36, 1], [12, 4, 1], [12, 24, 2], [12, 36, 1], [12, 72, 6], [16, 108, 4], [24, 36, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '864.2195', 'commutator_count': 1, 'commutator_label': '216.25', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 12235, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 1], [2, 72, 1, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [4, 72, 1, 1], [4, 72, 2, 1], [6, 2, 1, 1], [6, 18, 2, 1], [6, 24, 1, 1], [6, 72, 2, 1], [8, 18, 2, 1], [8, 36, 1, 1], [12, 4, 1, 1], [12, 24, 2, 1], [12, 36, 1, 1], [12, 72, 2, 1], [12, 72, 4, 1], [16, 108, 4, 1], [24, 36, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 288, 'exponent': 48, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4]], 'familial': False, 'frattini_label': '12.2', 'frattini_quotient': '144.182', 'hash': 12235, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 8, 3, 3, 6], 'inner_gens': [[1, 438, 32, 64, 720], [445, 2, 128, 608, 1584], [33, 658, 16, 1200, 144], [1185, 1218, 592, 48, 144], [1153, 290, 16, 48, 144]], 'inner_hash': 2195, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': False, 'inner_tex': '(C_2\\times \\He_3).\\SD_{16}', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 6], [4, 2], [6, 8], [8, 8], [12, 6]], 'label': '1728.12235', 'linC_count': 16, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 2, 'linQ_dim': 14, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': '(C4*He3).SD16', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 38, 'number_divisions': 24, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 127, 'number_subgroup_classes': 127, 'number_subgroups': 2257, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 91], [3, 26], [4, 236], [6, 206], [8, 72], [12, 520], [16, 432], [24, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [432, 0], 'outer_gens': [[1, 1298, 16, 48, 144], [1, 2, 32, 672, 144]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 43, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 2], [6, 2], [8, 5], [12, 5], [32, 1], [48, 1]], 'representations': {'PC': {'code': 3042392072742955886946273535328187766980120783725347055323843045496644433122079407053849, 'gens': [1, 2, 5, 6, 7], 'pres': [9, -2, -2, -2, -2, -3, 3, -2, -2, -3, 7885, 46, 326, 74, 31395, 3918, 1444, 2893, 922, 211, 3461, 16430, 8663, 4568, 4091, 45366, 49911, 186, 103687, 51856, 214, 93320, 46673]}, 'Perm': {'d': 43, 'gens': [103051769102521726361107864058747403149383264216422, 140586915037552063253734078109681513362954036793569, 174652063397549908043361945803818962865981274141613, 4410517967741, 208918857227046410725795775456009378596421391480939, 5901334351082, 1546306431198056630058652294838848897230869262336000, 3053381643260330370887589682026615822877776261120000, 4492680797991609120023789961411117769433838833664000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_4\\times \\He_3).\\SD_{16}', 'transitive_degree': 288, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [12, 6, 12, 6, 8], 'aut_gens': [[1, 2, 16, 48, 144], [821, 710, 624, 608, 1008], [17, 486, 592, 704, 720], [1013, 150, 1248, 1168, 1008], [409, 1318, 688, 1248, 720], [773, 130, 1248, 1232, 1584]], 'aut_group': None, 'aut_hash': 2187308893640632527, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3456, 'aut_permdeg': 216, 'aut_perms': [5603060225526383134142276303093553422263230392186004662371031927011874072850863872447265703874416717487391363104214624332833032224073943075174376788745043411438477193674259249548728794691815000740400140511421542244318766072353647496489458182717602886110448869663277691753518055977790179823348819218028136749622511764142913023872700380173165716519281927356228415877362596993313726742883382107986411605301551796987, 9681315748443027962480390452081246070822147096765362667631119335722466526578018110238149495427532721876757951575059131723733255908149571672877428959963763688281239726303998723032145880258535167017425892216603562125040785874121671479871754196665329640982489006292014851471421690361022668558150157814422325268895699327077635385261142595662610054277475118773678721130531057424745713723064287862578405939943821468389, 831465534153733344948450210965887118143027200781097621931530464350196709871430780648566044493555724959951753325285386127278492558016962244142375992357103931874756583233320778037960646215530565514450051083215021381671027733597356658073346275881284146072578350122178588143891407782166998841717742598547902513952387299860393043237075577122201550825103335582121003211215171573648303225681687797554910189500210638547, 9239183502231379490779248497500063826335330193922907139291086419163926701263599569243845430306475519315716203036003010188606357134993443911643775802316682186671349940274527953328479422844199105413606230594077076707028186636984908940233878757628707481576724577466156669363702652035719630722268017110494830847430549624711242902874554098426597808580752659304195262094179363057931372341835361308392105258993332765735, 7673126080584001373759184784099883657677504954874445072423081863796230720343513486821279855674867601936573770266450879042716269413222415276056110641634529297361565407368519315808312674600736986342745608639270469495387900161469301530807695232011121553440518214461524780845172757915499374698916076436101373450978577613103081084957390366980239325245432020723951306467739207320313314584739600201823408026001368213167], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 1], [2, 72, 1, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [4, 72, 1, 1], [4, 72, 2, 1], [6, 2, 1, 1], [6, 18, 1, 2], [6, 24, 1, 1], [6, 72, 2, 1], [8, 18, 1, 2], [8, 36, 1, 1], [12, 4, 1, 1], [12, 24, 1, 2], [12, 36, 1, 1], [12, 72, 2, 3], [16, 108, 2, 2], [24, 36, 1, 4]], 'aut_supersolvable': False, 'aut_tex': '\\He_3.(C_2\\times C_4\\times D_4).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '864.3997', 'autcentquo_hash': 3997, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SU(3,2):C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 18, 1], [2, 72, 1], [3, 2, 1], [3, 24, 1], [4, 2, 1], [4, 18, 1], [4, 72, 3], [6, 2, 1], [6, 18, 2], [6, 24, 1], [6, 72, 2], [8, 18, 2], [8, 36, 1], [12, 4, 1], [12, 24, 2], [12, 36, 1], [12, 72, 6], [16, 108, 4], [24, 36, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '864.2195', 'commutator_count': 1, 'commutator_label': '216.25', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 12235, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 1], [2, 72, 1, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [4, 72, 1, 1], [4, 72, 2, 1], [6, 2, 1, 1], [6, 18, 2, 1], [6, 24, 1, 1], [6, 72, 2, 1], [8, 18, 2, 1], [8, 36, 1, 1], [12, 4, 1, 1], [12, 24, 2, 1], [12, 36, 1, 1], [12, 72, 2, 1], [12, 72, 4, 1], [16, 108, 4, 1], [24, 36, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 288, 'exponent': 48, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4]], 'familial': False, 'frattini_label': '12.2', 'frattini_quotient': '144.182', 'hash': 12235, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 8, 3, 3, 6], 'inner_gens': [[1, 438, 32, 64, 720], [445, 2, 128, 608, 1584], [33, 658, 16, 1200, 144], [1185, 1218, 592, 48, 144], [1153, 290, 16, 48, 144]], 'inner_hash': 2195, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': False, 'inner_tex': '(C_2\\times \\He_3).\\SD_{16}', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 6], [4, 2], [6, 8], [8, 8], [12, 6]], 'label': '1728.12235', 'linC_count': 16, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 2, 'linQ_dim': 14, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': '(C4*He3).SD16', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 38, 'number_divisions': 24, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 127, 'number_subgroup_classes': 127, 'number_subgroups': 2257, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 91], [3, 26], [4, 236], [6, 206], [8, 72], [12, 520], [16, 432], [24, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [432, 0], 'outer_gens': [[1, 1298, 16, 48, 144], [1, 2, 32, 672, 144]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 43, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 2], [6, 2], [8, 5], [12, 5], [32, 1], [48, 1]], 'representations': {'PC': {'code': 3042392072742955886946273535328187766980120783725347055323843045496644433122079407053849, 'gens': [1, 2, 5, 6, 7], 'pres': [9, -2, -2, -2, -2, -3, 3, -2, -2, -3, 7885, 46, 326, 74, 31395, 3918, 1444, 2893, 922, 211, 3461, 16430, 8663, 4568, 4091, 45366, 49911, 186, 103687, 51856, 214, 93320, 46673]}, 'Perm': {'d': 43, 'gens': [103051769102521726361107864058747403149383264216422, 140586915037552063253734078109681513362954036793569, 174652063397549908043361945803818962865981274141613, 4410517967741, 208918857227046410725795775456009378596421391480939, 5901334351082, 1546306431198056630058652294838848897230869262336000, 3053381643260330370887589682026615822877776261120000, 4492680797991609120023789961411117769433838833664000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_4\\times \\He_3).\\SD_{16}', 'transitive_degree': 288, 'wreath_data': None, 'wreath_product': False}
