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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.105', 'ambient_counter': 105, 'ambient_order': 1056, 'ambient_tex': 'C_{33}:Q_{32}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 22, 'counter': 31, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.105.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_8', 'simple': False, 'solvable': True, 'special_labels': ['L3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1056.105', 'aut_centralizer_order': 1408, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 1408, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'contains': ['96.a1.a1', '528.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7672, 2053, 1513, 2048, 1760, 4181, 2288, 4181], 'generators': [16, 96], 'label': '1056.105.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '528.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.10', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '22.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 10, 'aut_gen_orders': [10], 'aut_gens': [[1], [13]], 'aut_group': '10.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 10, 'aut_permdeg': 7, 'aut_perms': [753], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [11, 1, 10, 1], [22, 1, 10, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{10}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 10, 'autcent_group': '10.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 10, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{10}', '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], [11, 1, 10], [22, 1, 10]], 'center_label': '22.2', 'center_order': 22, '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', '11.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [11, 1, 10, 1], [22, 1, 10, 1]], 'element_repr_type': 'PC', 'elementary': 22, 'eulerian_function': 1, 'exponent': 22, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 11], 'faithful_reps': [[1, 0, 10]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '22.2', 'hash': 2, 'hyperelementary': 22, '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': 10, 'irrQ_dim': 10, 'irrR_degree': 2, 'irrep_stats': [[1, 22]], 'label': '22.2', 'linC_count': 10, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 1, 'linQ_dim': 10, 'linQ_dim_count': 1, 'linR_count': 5, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C22', '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': 22, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 22, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [11, 10], [22, 10]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [10], 'outer_gen_pows': [0], 'outer_gens': [[13]], 'outer_group': '10.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 10, 'outer_permdeg': 7, 'outer_perms': [753], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{10}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [10, 2]], 'representations': {'PC': {'code': 509, 'gens': [1], 'pres': [2, -2, -11, 4]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [1343, 13320]}, 'Perm': {'d': 13, 'gens': [479001600, 36288000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [22], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{22}', 'transitive_degree': 22, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 440, 'aut_gen_orders': [40, 20, 44, 4, 22, 20], 'aut_gens': [[1, 2, 32], [5, 970, 448], [17, 502, 800], [5, 406, 736], [25, 602, 1024], [5, 894, 32], [21, 6, 512]], 'aut_group': None, 'aut_hash': 4385543647610386797, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 14080, 'aut_permdeg': 98, 'aut_perms': [2235440556856493626018161952293911036848270313290364982049302649511188486583932442299982520630249786166993533913036721904949169366785081392478379405908399, 5676796910890738224859742739333600446233002039773244669936162233910774483195093332950423262733013857313344787553825757899785553357539714790241527518011868, 2272826062458477022352872755559008426297281622344717644157486057093419055201499901455764653223967192786031885136135981886860449077780677792492706785974326, 154096505505038493793838049220388241411864397230096773428814287439066250036297663097206895810826767651166269914221274435941740298996751701141192149291373, 2272215918089557415835982758997941395109839761071583355536625940529497619168478618276238756775310456550168782677062371464030888646662770902823648922161063, 7912122522097575421918709586345868751427369428609456767363064336156936271699544994901800432791333885792865766599061147414744086499183847993796306198283966], 'aut_phi_ratio': 44.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 2, 1, 1], [4, 8, 1, 1], [4, 88, 1, 1], [6, 1, 2, 1], [8, 2, 2, 1], [11, 2, 5, 1], [12, 2, 2, 1], [12, 8, 2, 1], [12, 88, 2, 1], [16, 22, 4, 1], [22, 2, 5, 1], [24, 2, 4, 1], [33, 2, 10, 1], [44, 4, 5, 1], [44, 8, 10, 1], [48, 22, 8, 1], [66, 2, 10, 1], [88, 4, 10, 1], [132, 4, 10, 1], [132, 8, 20, 1], [264, 4, 20, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{44}.(C_2^4\\times C_{20})', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '1760.1090', 'autcentquo_hash': 1090, 'autcentquo_nilpotent': False, 'autcentquo_order': 1760, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_4\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [4, 2, 1], [4, 8, 1], [4, 88, 1], [6, 1, 2], [8, 2, 2], [11, 2, 5], [12, 2, 2], [12, 8, 2], [12, 88, 2], [16, 22, 4], [22, 2, 5], [24, 2, 4], [33, 2, 10], [44, 4, 5], [44, 8, 10], [48, 22, 8], [66, 2, 10], [88, 4, 10], [132, 4, 10], [132, 8, 20], [264, 4, 20]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '176.14', 'commutator_count': 1, 'commutator_label': '88.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 105, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['352.35', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 2, 1, 1], [4, 8, 1, 1], [4, 88, 1, 1], [6, 1, 2, 1], [8, 2, 2, 1], [11, 2, 5, 1], [12, 2, 2, 1], [12, 8, 2, 1], [12, 88, 2, 1], [16, 22, 4, 1], [22, 2, 5, 1], [24, 2, 4, 1], [33, 2, 10, 1], [44, 4, 5, 1], [44, 8, 10, 1], [48, 22, 8, 1], [66, 2, 10, 1], [88, 4, 10, 1], [132, 4, 10, 1], [132, 8, 20, 1], [264, 4, 20, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 528, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[4, 0, 20]], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '132.7', 'hash': 105, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 88, 'inner_gen_orders': [2, 8, 11], 'inner_gens': [[1, 30, 32], [5, 2, 320], [1, 770, 32]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 176, 'inner_split': True, 'inner_tex': 'C_{11}:D_8', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 80, 'irrQ_dim': 160, 'irrR_degree': 8, 'irrep_stats': [[1, 12], [2, 81], [4, 45]], 'label': '1056.105', 'linC_count': 660, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 8, 'linQ_dim': 26, 'linQ_dim_count': 2, 'linR_count': 40, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C33:Q32', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 138, 'number_divisions': 24, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 48, 'number_subgroups': 260, 'old_label': None, 'order': 1056, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 98], [6, 2], [8, 4], [11, 10], [12, 196], [16, 88], [22, 10], [24, 8], [33, 20], [44, 100], [48, 176], [66, 20], [88, 40], [132, 200], [264, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 20, 'outer_gen_orders': [2, 2, 20], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 2, 1024], [17, 2, 320], [1, 10, 800]], 'outer_group': '80.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 80, 'outer_permdeg': 13, 'outer_perms': [479001600, 3669840, 131073], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{20}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 46, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 2], [8, 2], [10, 2], [16, 1], [20, 4], [40, 3], [80, 1]], 'representations': {'PC': {'code': 19731774974579113872027093338948571990000019, 'gens': [1, 2, 6], 'pres': [7, -2, -2, -2, -2, -2, -3, -11, 112, 421, 36, 590, 58, 675, 80, 6732, 166, 23533]}, 'Perm': {'d': 46, 'gens': [2659677397344879506642652416570148233569585007914837782, 17811145675098381013279821101681975, 303916116658416027343136804044800000000, 26343719457735960423234576311500899, 34840859341686435002182202060144884, 43338190687606480833908607840527599, 124941575660169581581902960218859457508042971545600000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{33}:Q_{32}', 'transitive_degree': 1056, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 8, 'aut_gen_orders': [2, 2, 2, 8], 'aut_gens': [[1, 2], [25, 34], [1, 26], [37, 14], [19, 2]], 'aut_group': '64.254', 'aut_hash': 254, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 64, 'aut_permdeg': 10, 'aut_perms': [2687455, 85800, 2324448, 2071609], 'aut_phi_ratio': 4.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 2, 1], [3, 1, 2, 1], [4, 2, 1, 1], [6, 1, 2, 1], [6, 4, 4, 1], [8, 2, 2, 1], [12, 2, 2, 1], [24, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_8:C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '8.3', 'autcentquo_hash': 3, 'autcentquo_nilpotent': True, 'autcentquo_order': 8, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 2], [3, 1, 2], [4, 2, 1], [6, 1, 2], [6, 4, 4], [8, 2, 2], [12, 2, 2], [24, 2, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '8.3', 'commutator_count': 1, 'commutator_label': '4.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 25, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.7', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 2], [3, 1, 2, 1], [4, 2, 1, 1], [6, 1, 2, 1], [6, 4, 2, 2], [8, 2, 2, 1], [12, 2, 2, 1], [24, 2, 4, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 12, 'exponent': 24, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 4]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '12.5', 'hash': 25, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4], 'inner_gens': [[1, 14], [37, 2]], 'inner_hash': 3, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'D_4', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 12], [2, 9]], 'label': '48.25', 'linC_count': 4, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 4, 'linQ_dim': 6, 'linQ_dim_count': 4, 'linR_count': 10, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*D8', 'ngens': 5, 'nilpotency_class': 3, '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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 21, 'number_divisions': 12, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 22, 'number_subgroups': 38, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 9], [3, 2], [4, 2], [6, 18], [8, 4], [12, 4], [24, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 46], 'outer_gens': [[1, 34], [1, 26], [7, 2]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 2], [8, 1]], 'representations': {'PC': {'code': 11655680362433, 'gens': [1, 2], 'pres': [5, -2, -2, -2, -2, -3, 141, 26, 422, 42, 58]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101739150932828, 41624325029299721]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [2059, 1628]}, 'Perm': {'d': 11, 'gens': [16148160, 42744, 4, 11613864, 3669864]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times D_8', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
