LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-10-11T17:08:43.357399

Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
abelian_quotient	text
all_subgroups_known	boolean
almost_simple	boolean
aut_abelian	boolean
aut_cyclic	boolean
aut_derived_length	smallint
aut_exponent	numeric
aut_gen_orders	numeric[]
aut_gens	numeric[]
aut_group	text
aut_hash	bigint
aut_nilpotency_class	smallint
aut_nilpotent	boolean
aut_order	numeric
aut_permdeg	integer
aut_perms	numeric[]
aut_phi_ratio	double precision
aut_solvable	boolean
aut_stats	numeric[]
aut_supersolvable	boolean
aut_tex	text
autcent_abelian	boolean
autcent_cyclic	boolean
autcent_exponent	numeric
autcent_group	text
autcent_hash	bigint
autcent_nilpotent	boolean
autcent_order	numeric
autcent_solvable	boolean
autcent_split	boolean
autcent_supersolvable	boolean
autcent_tex	text
autcentquo_abelian	boolean
autcentquo_cyclic	boolean
autcentquo_exponent	numeric
autcentquo_group	text
autcentquo_hash	bigint
autcentquo_nilpotent	boolean
autcentquo_order	numeric
autcentquo_solvable	boolean
autcentquo_supersolvable	boolean
autcentquo_tex	text
cc_stats	numeric[]
center_label	text
center_order	numeric
central_product	boolean
central_quotient	text
commutator_count	integer
commutator_label	text
complements_known	boolean
complete	boolean
complex_characters_known	boolean
composition_factors	text[]
composition_length	smallint
conjugacy_classes_known	boolean
counter	integer
cyclic	boolean
derived_length	smallint
dihedral	boolean
direct_factorization	jsonb
direct_product	boolean
div_stats	numeric[]
element_repr_type	text
elementary	integer
eulerian_function	numeric
exponent	numeric
exponents_of_order	smallint[]
factors_of_aut_order	integer[]
factors_of_order	smallint[]
faithful_reps	numeric[]
familial	boolean
frattini_label	text
frattini_quotient	text
hash	bigint
hyperelementary	integer
inner_abelian	boolean
inner_cyclic	boolean
inner_exponent	numeric
inner_gen_orders	numeric[]
inner_gens	numeric[]
inner_hash	bigint
inner_nilpotent	boolean
inner_order	numeric
inner_split	boolean
inner_tex	text
inner_used	smallint[]
irrC_degree	integer
irrQ_degree	integer
irrQ_dim	integer
irrR_degree	integer
irrep_stats	numeric[]
label	text
linC_count	numeric
linC_degree	integer
linFp_degree	integer
linFq_degree	integer
linQ_degree	integer
linQ_degree_count	numeric
linQ_dim	integer
linQ_dim_count	numeric
linR_count	numeric
linR_degree	integer
maximal_subgroups_known	boolean
metabelian	boolean
metacyclic	boolean
monomial	boolean
name	text
ngens	smallint
nilpotency_class	smallint
nilpotent	boolean
normal_counts	integer[]
normal_index_bound	numeric
normal_order_bound	numeric
normal_subgroups_known	boolean
number_autjugacy_classes	integer
number_characteristic_subgroups	integer
number_conjugacy_classes	integer
number_divisions	integer
number_normal_subgroups	integer
number_subgroup_autclasses	integer
number_subgroup_classes	integer
number_subgroups	numeric
old_label	text
order	numeric
order_factorization_type	integer
order_stats	numeric[]
outer_abelian	boolean
outer_cyclic	boolean
outer_equivalence	boolean
outer_exponent	numeric
outer_gen_orders	numeric[]
outer_gen_pows	numeric[]
outer_gens	numeric[]
outer_group	text
outer_hash	bigint
outer_nilpotent	boolean
outer_order	numeric
outer_permdeg	integer
outer_perms	numeric[]
outer_solvable	boolean
outer_supersolvable	boolean
outer_tex	text
pc_rank	smallint
perfect	boolean
permutation_degree	integer
pgroup	smallint
primary_abelian_invariants	integer[]
quasisimple	boolean
rank	smallint
rational	boolean
rational_characters_known	boolean
ratrep_stats	numeric[]
representations	jsonb
schur_multiplier	integer[]
semidirect_product	boolean
simple	boolean
smith_abelian_invariants	integer[]
solvability_type	smallint
solvable	boolean
subgroup_inclusions_known	boolean
subgroup_index_bound	numeric
supersolvable	boolean
sylow_subgroups_known	boolean
tex_name	text
transitive_degree	integer
wreath_data	text[]
wreath_product	boolean

gps_groups • Show schema

{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6510, 'aut_gen_orders': [30, 30, 10], 'aut_gens': [[1, 6], [187, 246], [943, 1206], [421, 1212]], 'aut_group': None, 'aut_hash': 4525314779087553066, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 39060, 'aut_permdeg': 224, 'aut_perms': [23051822460664836511067489594416055473295664929227983938704715278444488581879999914241023098684184206240000060768359135891426573473369419980819823349042553930494741893724396830944213042915678832494033375199220543400764591764719092604253568407470822982880388552231069321410521958690822334737221783874819496450198206193579655607948141202438814240063145739295519601270765405197564154792359172288658929491967377868597623716297959846493, 1533391175239681607720735653099297821072502154286680853056037634817398182458171371204421314082820685439046099578502442652685723491091397128913089111883354683741380448327354024447218099646339256729724677597678055328772490015974472599388438041705080625850775943361596625535752429027456607234325957512370806579274100423110766307834357628308530322024120099617530036728731139253064990960824804828770246114193019003615185415407160784003, 55544066088710889900441272552298181957962743953764840074878712738207854952251623208891351177341616467064513789694369514587938212775789417510457952110040230909074590282158537323809136908443588342393878382120100161984690378481576866688451259545723919100280961582334811979290315359716522628357043003613453419315390713177721906526883964489180169491044676127901960722339275155586365769510133285615911304768853689327233949500405953290794], 'aut_phi_ratio': 108.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 217, 1, 2], [6, 217, 1, 2], [7, 6, 1, 1], [31, 3, 10, 1], [62, 21, 10, 1], [217, 6, 30, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{31}:(C_{30}\\times F_7)', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6510, 'autcentquo_group': None, 'autcentquo_hash': 4525314779087553066, 'autcentquo_nilpotent': False, 'autcentquo_order': 39060, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{31}:(C_{30}\\times F_7)', 'cc_stats': [[1, 1, 1], [2, 7, 1], [3, 217, 2], [6, 217, 2], [7, 6, 1], [31, 3, 10], [62, 21, 10], [217, 6, 30]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1302.10', 'commutator_count': 1, 'commutator_label': '217.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '7.1', '31.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 217, 2, 1], [6, 217, 2, 1], [7, 6, 1, 1], [31, 3, 10, 1], [62, 21, 10, 1], [217, 6, 30, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 1302, 'exponents_of_order': [1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7, 31], 'factors_of_order': [2, 3, 7, 31], 'faithful_reps': [[6, 0, 30]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1302.10', 'hash': 10, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 1302, 'inner_gen_orders': [6, 217], 'inner_gens': [[1, 774], [535, 6]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 1302, 'inner_split': True, 'inner_tex': 'C_{217}:C_6', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 180, 'irrQ_dim': 180, 'irrR_degree': 12, 'irrep_stats': [[1, 6], [3, 20], [6, 31]], 'label': '1302.10', 'linC_count': 30, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 36, 'linQ_degree_count': 2, 'linQ_dim': 36, 'linQ_dim_count': 2, 'linR_count': 25, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C217:C6', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 57, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 16, 'number_subgroups': 532, 'old_label': None, 'order': 1302, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 7], [3, 434], [6, 434], [7, 6], [31, 30], [62, 210], [217, 180]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [30], 'outer_gen_pows': [0], 'outer_gens': [[1, 132]], 'outer_group': '30.4', 'outer_hash': 4, 'outer_nilpotent': True, 'outer_order': 30, 'outer_permdeg': 10, 'outer_perms': [372993], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{30}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 38, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [6, 1], [30, 2], [180, 1]], 'representations': {'PC': {'code': 37302960262044194763571079, 'gens': [1, 3], 'pres': [4, -2, -3, -7, -31, 8, 9290, 5370, 94, 3363, 8407]}, 'Perm': {'d': 38, 'gens': [136, 393546416358345675989788906010348626978885, 1103, 14539956220081886392842823538923044496896000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{217}:C_6', 'transitive_degree': 217, 'wreath_data': None, 'wreath_product': False}

Column	Type
aut_label	text
centralizer	text
counter	integer
group_counter	integer
group_order	numeric
label	text
order	integer
powers	integer[]
representative	numeric
size	numeric

gps_conj_classes • Show schema

id: 114956955
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 10, 'group_order': 1302, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1, 1], 'representative': 0, 'size': 1}
id: 114956966
{'aut_label': '2A', 'centralizer': '7.a1.a1', 'counter': 2, 'group_counter': 10, 'group_order': 1302, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2, 2], 'representative': 3, 'size': 7}
id: 114956977
{'aut_label': '3A1', 'centralizer': '217.a1.a1', 'counter': 3, 'group_counter': 10, 'group_order': 1302, 'label': '3A1', 'order': 3, 'powers': [4, 1, 4, 3, 3], 'representative': 556, 'size': 217}
id: 114956988
{'aut_label': '3A-1', 'centralizer': '217.a1.a1', 'counter': 4, 'group_counter': 10, 'group_order': 1302, 'label': '3A-1', 'order': 3, 'powers': [3, 1, 3, 4, 4], 'representative': 1082, 'size': 217}
id: 114956999
{'aut_label': '6A1', 'centralizer': '217.a1.a1', 'counter': 5, 'group_counter': 10, 'group_order': 1302, 'label': '6A1', 'order': 6, 'powers': [3, 2, 6, 5, 5], 'representative': 713, 'size': 217}
id: 114957008
{'aut_label': '6A-1', 'centralizer': '217.a1.a1', 'counter': 6, 'group_counter': 10, 'group_order': 1302, 'label': '6A-1', 'order': 6, 'powers': [4, 2, 5, 6, 6], 'representative': 1111, 'size': 217}
id: 114957009
{'aut_label': '7A', 'centralizer': '6.a1.a1', 'counter': 7, 'group_counter': 10, 'group_order': 1302, 'label': '7A', 'order': 7, 'powers': [7, 7, 7, 1, 7], 'representative': 186, 'size': 6}
id: 114957010
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 8, 'group_counter': 10, 'group_order': 1302, 'label': '31A1', 'order': 31, 'powers': [10, 12, 8, 14, 1], 'representative': 84, 'size': 3}
id: 114957011
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 9, 'group_counter': 10, 'group_order': 1302, 'label': '31A-1', 'order': 31, 'powers': [11, 13, 9, 15, 1], 'representative': 1218, 'size': 3}
id: 114956956
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 10, 'group_counter': 10, 'group_order': 1302, 'label': '31A2', 'order': 31, 'powers': [14, 9, 10, 16, 1], 'representative': 168, 'size': 3}
id: 114956957
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 11, 'group_counter': 10, 'group_order': 1302, 'label': '31A-2', 'order': 31, 'powers': [15, 8, 11, 17, 1], 'representative': 1134, 'size': 3}
id: 114956958
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 12, 'group_counter': 10, 'group_order': 1302, 'label': '31A3', 'order': 31, 'powers': [9, 16, 12, 11, 1], 'representative': 252, 'size': 3}
id: 114956959
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 13, 'group_counter': 10, 'group_order': 1302, 'label': '31A-3', 'order': 31, 'powers': [8, 17, 13, 10, 1], 'representative': 1050, 'size': 3}
id: 114956960
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 14, 'group_counter': 10, 'group_order': 1302, 'label': '31A4', 'order': 31, 'powers': [16, 11, 14, 13, 1], 'representative': 336, 'size': 3}
id: 114956961
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 15, 'group_counter': 10, 'group_order': 1302, 'label': '31A-4', 'order': 31, 'powers': [17, 10, 15, 12, 1], 'representative': 966, 'size': 3}
id: 114956962
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 16, 'group_counter': 10, 'group_order': 1302, 'label': '31A8', 'order': 31, 'powers': [13, 15, 16, 8, 1], 'representative': 672, 'size': 3}
id: 114956963
{'aut_label': '31A1', 'centralizer': '3.a1.a1', 'counter': 17, 'group_counter': 10, 'group_order': 1302, 'label': '31A-8', 'order': 31, 'powers': [12, 14, 17, 9, 1], 'representative': 630, 'size': 3}
id: 114956964
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 18, 'group_counter': 10, 'group_order': 1302, 'label': '62A1', 'order': 62, 'powers': [8, 20, 18, 22, 2], 'representative': 45, 'size': 21}
id: 114956965
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 19, 'group_counter': 10, 'group_order': 1302, 'label': '62A-1', 'order': 62, 'powers': [9, 21, 19, 23, 2], 'representative': 255, 'size': 21}
id: 114956967
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 20, 'group_counter': 10, 'group_order': 1302, 'label': '62A3', 'order': 62, 'powers': [12, 24, 20, 27, 2], 'representative': 129, 'size': 21}
id: 114956968
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 21, 'group_counter': 10, 'group_order': 1302, 'label': '62A-3', 'order': 62, 'powers': [13, 25, 21, 26, 2], 'representative': 15, 'size': 21}
id: 114956969
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 22, 'group_counter': 10, 'group_order': 1302, 'label': '62A7', 'order': 62, 'powers': [14, 27, 22, 21, 2], 'representative': 171, 'size': 21}
id: 114956970
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 23, 'group_counter': 10, 'group_order': 1302, 'label': '62A-7', 'order': 62, 'powers': [15, 26, 23, 20, 2], 'representative': 21, 'size': 21}
id: 114956971
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 24, 'group_counter': 10, 'group_order': 1302, 'label': '62A9', 'order': 62, 'powers': [16, 23, 24, 18, 2], 'representative': 9, 'size': 21}
id: 114956972
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 25, 'group_counter': 10, 'group_order': 1302, 'label': '62A-9', 'order': 62, 'powers': [17, 22, 25, 19, 2], 'representative': 39, 'size': 21}
id: 114956973
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 26, 'group_counter': 10, 'group_order': 1302, 'label': '62A19', 'order': 62, 'powers': [10, 19, 26, 24, 2], 'representative': 87, 'size': 21}
id: 114956974
{'aut_label': '62A1', 'centralizer': '21.a1.a1', 'counter': 27, 'group_counter': 10, 'group_order': 1302, 'label': '62A-19', 'order': 62, 'powers': [11, 18, 27, 25, 2], 'representative': 507, 'size': 21}
id: 114956975
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 28, 'group_counter': 10, 'group_order': 1302, 'label': '217A1', 'order': 217, 'powers': [30, 32, 36, 13, 7], 'representative': 6, 'size': 6}
id: 114956976
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 29, 'group_counter': 10, 'group_order': 1302, 'label': '217A-1', 'order': 217, 'powers': [31, 33, 37, 12, 7], 'representative': 222, 'size': 6}
id: 114956978
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 30, 'group_counter': 10, 'group_order': 1302, 'label': '217A2', 'order': 217, 'powers': [34, 37, 42, 8, 7], 'representative': 12, 'size': 6}
id: 114956979
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 31, 'group_counter': 10, 'group_order': 1302, 'label': '217A-2', 'order': 217, 'powers': [35, 36, 43, 9, 7], 'representative': 444, 'size': 6}
id: 114956980
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 32, 'group_counter': 10, 'group_order': 1302, 'label': '217A3', 'order': 217, 'powers': [37, 40, 46, 17, 7], 'representative': 18, 'size': 6}
id: 114956981
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 33, 'group_counter': 10, 'group_order': 1302, 'label': '217A-3', 'order': 217, 'powers': [36, 41, 47, 16, 7], 'representative': 96, 'size': 6}
id: 114956982
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 34, 'group_counter': 10, 'group_order': 1302, 'label': '217A4', 'order': 217, 'powers': [38, 43, 50, 10, 7], 'representative': 24, 'size': 6}
id: 114956983
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 35, 'group_counter': 10, 'group_order': 1302, 'label': '217A-4', 'order': 217, 'powers': [39, 42, 51, 11, 7], 'representative': 330, 'size': 6}
id: 114956984
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 36, 'group_counter': 10, 'group_order': 1302, 'label': '217A5', 'order': 217, 'powers': [42, 46, 52, 13, 7], 'representative': 30, 'size': 6}
id: 114956985
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 37, 'group_counter': 10, 'group_order': 1302, 'label': '217A-5', 'order': 217, 'powers': [43, 47, 53, 12, 7], 'representative': 36, 'size': 6}
id: 114956986
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 38, 'group_counter': 10, 'group_order': 1302, 'label': '217A8', 'order': 217, 'powers': [33, 51, 40, 14, 7], 'representative': 48, 'size': 6}
id: 114956987
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 39, 'group_counter': 10, 'group_order': 1302, 'label': '217A-8', 'order': 217, 'powers': [32, 50, 41, 15, 7], 'representative': 318, 'size': 6}
id: 114956989
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 40, 'group_counter': 10, 'group_order': 1302, 'label': '217A9', 'order': 217, 'powers': [47, 44, 49, 14, 7], 'representative': 54, 'size': 6}
id: 114956990
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 41, 'group_counter': 10, 'group_order': 1302, 'label': '217A-9', 'order': 217, 'powers': [46, 45, 48, 15, 7], 'representative': 288, 'size': 6}
id: 114956991
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 42, 'group_counter': 10, 'group_order': 1302, 'label': '217A10', 'order': 217, 'powers': [50, 53, 57, 8, 7], 'representative': 60, 'size': 6}
id: 114956992
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 43, 'group_counter': 10, 'group_order': 1302, 'label': '217A-10', 'order': 217, 'powers': [51, 52, 56, 9, 7], 'representative': 174, 'size': 6}
id: 114956993
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 44, 'group_counter': 10, 'group_order': 1302, 'label': '217A11', 'order': 217, 'powers': [48, 30, 35, 11, 7], 'representative': 66, 'size': 6}
id: 114956994
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 45, 'group_counter': 10, 'group_order': 1302, 'label': '217A-11', 'order': 217, 'powers': [49, 31, 34, 10, 7], 'representative': 600, 'size': 6}
id: 114956995
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 46, 'group_counter': 10, 'group_order': 1302, 'label': '217A15', 'order': 217, 'powers': [53, 49, 54, 17, 7], 'representative': 90, 'size': 6}
id: 114956996
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 47, 'group_counter': 10, 'group_order': 1302, 'label': '217A-15', 'order': 217, 'powers': [52, 48, 55, 16, 7], 'representative': 108, 'size': 6}
id: 114956997
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 48, 'group_counter': 10, 'group_order': 1302, 'label': '217A17', 'order': 217, 'powers': [54, 34, 39, 15, 7], 'representative': 132, 'size': 6}
id: 114956998
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 49, 'group_counter': 10, 'group_order': 1302, 'label': '217A-17', 'order': 217, 'powers': [55, 35, 38, 14, 7], 'representative': 270, 'size': 6}
id: 114957000
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 50, 'group_counter': 10, 'group_order': 1302, 'label': '217A20', 'order': 217, 'powers': [40, 56, 45, 10, 7], 'representative': 228, 'size': 6}
id: 114957001
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 51, 'group_counter': 10, 'group_order': 1302, 'label': '217A-20', 'order': 217, 'powers': [41, 57, 44, 11, 7], 'representative': 144, 'size': 6}
id: 114957002
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 52, 'group_counter': 10, 'group_order': 1302, 'label': '217A25', 'order': 217, 'powers': [57, 54, 28, 13, 7], 'representative': 216, 'size': 6}
id: 114957003
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 53, 'group_counter': 10, 'group_order': 1302, 'label': '217A-25', 'order': 217, 'powers': [56, 55, 29, 12, 7], 'representative': 180, 'size': 6}
id: 114957004
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 54, 'group_counter': 10, 'group_order': 1302, 'label': '217A34', 'order': 217, 'powers': [29, 38, 32, 17, 7], 'representative': 264, 'size': 6}
id: 114957005
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 55, 'group_counter': 10, 'group_order': 1302, 'label': '217A-34', 'order': 217, 'powers': [28, 39, 33, 16, 7], 'representative': 540, 'size': 6}
id: 114957006
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 56, 'group_counter': 10, 'group_order': 1302, 'label': '217A43', 'order': 217, 'powers': [44, 28, 31, 9, 7], 'representative': 258, 'size': 6}
id: 114957007
{'aut_label': '217A1', 'centralizer': '6.a1.a1', 'counter': 57, 'group_counter': 10, 'group_order': 1302, 'label': '217A-43', 'order': 217, 'powers': [45, 29, 30, 8, 7], 'representative': 300, 'size': 6}

Column	Type
cdim	integer
counter	smallint
faithful	boolean
group	text
group_order	numeric
image	text
label	text
multiplicity	smallint
nt	integer[]
qdim	integer
qvalues	integer[]
schur_index	smallint

gps_qchar • Show schema

id: 5527622
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 5527623
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 5527624
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
id: 5527625
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
id: 5527628
{'cdim': 6, 'counter': 7, 'faithful': False, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.6a', 'multiplicity': 1, 'nt': [7, 4], 'qdim': 6, 'qvalues': [6, 0, 0, 0, 0, 0, -1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 5527626
{'cdim': 3, 'counter': 5, 'faithful': False, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.3a', 'multiplicity': 10, 'nt': [31, 3], 'qdim': 30, 'qvalues': [30, 30, 0, 0, 0, 0, 30, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 5527627
{'cdim': 3, 'counter': 6, 'faithful': False, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.3b', 'multiplicity': 10, 'nt': [62, 0], 'qdim': 30, 'qvalues': [30, -30, 0, 0, 0, 0, 30, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 5527629
{'cdim': 6, 'counter': 8, 'faithful': True, 'group': '1302.10', 'group_order': 1302, 'image': None, 'label': '1302.10.6b', 'multiplicity': 30, 'nt': [217, 0], 'qdim': 180, 'qvalues': [180, 0, 0, 0, 0, 0, -30, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}

Column	Type
center	text
center_index	numeric
center_order	numeric
counter	smallint
cyclotomic_n	integer
dim	integer
faithful	boolean
field	numeric[]
group	text
group_counter	integer
group_order	numeric
image	text
image_isoclass	text
image_order	numeric
indicator	smallint
kernel	text
kernel_order	numeric
label	text
nt	integer[]
q_character	text
values	jsonb

gps_char • Show schema

id: 10800112
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1302, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1302.10', 'group_counter': 10, 'group_order': 1302, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1302, 'label': '1302.10.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10800123
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1302, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1302.10', 'group_counter': 10, 'group_order': 1302, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 651, 'label': '1302.10.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10800134
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1302, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1302.10', 'group_counter': 10, 'group_order': 1302, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 434, 'label': '1302.10.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10800145
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1302, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1302.10', 'group_counter': 10, 'group_order': 1302, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 434, 'label': '1302.10.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10800156
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1302, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1302.10', 'group_counter': 10, 'group_order': 1302, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 217, 'label': '1302.10.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10800165
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1302, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1302.10', 'group_counter': 10, 'group_order': 1302, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 217, 'label': '1302.10.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10800166
{'center': '93.a1.a1', 'center_index': 93, 'center_order': 14, 'counter': 7, 'cyclotomic_n': 31, 'dim': 3, 'faithful': False, 'field': [25, -20, 63, -6, 43, 11, -9, 16, 2, -1, 1], 'group': '1302.10', 'group_counter': 10, 'group_order': 1302, 'image': None, 'image_isoclass': '93.1', 'image_order': 93, 'indicator': 0, 'kernel': '93.a1.a1', 'kernel_order': 14, 'label': '1302.10.3a1', 'nt': [31, 3], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, -14], [1, -9], [1, -8]], [[1, 8], [1, 9], [1, 14]], [[1, 3], [1, 13], [1, 15]], [[1, 2], [1, 10], [1, -12]], [[1, 1], [1, 5], [1, -6]], [[1, 11], [1, -7], [1, -4]], [[1, 6], [1, -5], [1, -1]], [[1, 4], [1, 7], [1, -11]], [[1, 12], [1, -10], [1, -2]], [[1, -15], [1, -13], [1, -3]], [[1, -15], [1, -13], [1, -3]], [[1, 1], [1, 5], [1, -6]], [[1, 8], [1, 9], [1, 14]], [[1, -14], [1, -9], [1, -8]], [[1, 3], [1, 13], [1, 15]], [[1, 11], [1, -7], [1, -4]], [[1, 6], [1, -5], [1, -1]], [[1, 4], [1, 7], [1, -11]], [[1, 12], [1, -10], [1, -2]], [[1, 2], [1, 10], [1, -12]], [[1, 11], [1, -7], [1, -4]], [[1, -15], [1, -13], [1, -3]], [[1, 1], [1, 5], [1, -6]], [[1, -15], [1, -13], [1, -3]], [[1, 3], [1, 13], [1, 15]], [[1, 11], [1, -7], [1, -4]], [[1, 2], [1, 10], [1, -12]], [[1, 6], [1, -5], [1, -1]], [[1, 4], [1, 7], [1, -11]], [[1, 12], [1, -10], [1, -2]], [[1, -15], [1, -13], [1, -3]], [[1, 8], [1, 9], [1, 14]], [[1, 3], [1, 13], [1, 15]], [[1, 4], [1, 7], [1, -11]], [[1, -14], [1, -9], [1, -8]], [[1, 3], [1, 13], [1, 15]], [[1, 2], [1, 10], [1, -12]], [[1, 1], [1, 5], [1, -6]], [[1, -14], [1, -9], [1, -8]], [[1, 6], [1, -5], [1, -1]], [[1, 1], [1, 5], [1, -6]], [[1, 6], [1, -5], [1, -1]], [[1, 12], [1, -10], [1, -2]], [[1, 12], [1, -10], [1, -2]], [[1, 11], [1, -7], [1, -4]], [[1, 4], [1, 7], [1, -11]], [[1, 2], [1, 10], [1, -12]], [[1, 8], [1, 9], [1, 14]], [[1, -14], [1, -9], [1, -8]], [[1, 8], [1, 9], [1, 14]]]}
id: 10800119
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id: 10800167
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id: 10800168
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id: 10800113
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id: 10800114
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id: 10800115
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id: 10800116
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id: 10800117
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id: 10800118
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id: 10800120
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id: 10800130
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id: 10800121
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id: 10800122
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id: 10800124
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id: 10800125
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id: 10800126
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id: 10800127
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id: 10800128
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id: 10800129
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id: 10800131
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id: 10800132
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id: 10800142
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id: 10800143
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id: 10800144
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id: 10800146
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id: 10800147
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id: 10800148
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id: 10800149
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id: 10800150
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id: 10800151
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id: 10800152
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id: 10800133
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id: 10800153
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id: 10800154
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id: 10800155
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id: 10800157
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id: 10800158
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id: 10800159
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id: 10800160
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id: 10800161
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id: 10800162
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id: 10800163
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id: 10800135
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id: 10800164
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id: 10800136
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id: 10800137
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id: 10800138
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id: 10800139
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id: 10800140
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id: 10800141
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Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
ambient	text
ambient_counter	integer
ambient_order	numeric
ambient_tex	text
central	boolean
central_factor	boolean
centralizer_order	numeric
characteristic	boolean
core_order	numeric
counter	integer
cyclic	boolean
direct	boolean
hall	numeric
label	text
maximal	boolean
maximal_normal	boolean
metabelian	boolean
metacyclic	boolean
minimal	boolean
minimal_normal	boolean
nilpotent	boolean
normal	boolean
old_label	text
outer_equivalence	boolean
perfect	boolean
proper	boolean
quotient	text
quotient_Agroup	boolean
quotient_abelian	boolean
quotient_cyclic	boolean
quotient_hash	bigint
quotient_metabelian	boolean
quotient_nilpotent	boolean
quotient_order	numeric
quotient_simple	boolean
quotient_solvable	boolean
quotient_supersolvable	boolean
quotient_tex	text
simple	boolean
solvable	boolean
special_labels	text[]
split	boolean
standard_generators	boolean
stem	boolean
subgroup	text
subgroup_hash	bigint
subgroup_order	numeric
subgroup_tex	text
supersolvable	boolean
sylow	smallint

gps_subgroup_search • Show schema

id: 71243912
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1302, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 1302, 'label': '1302.10.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1302.10', 'subgroup_hash': 10, 'subgroup_order': 1302, 'subgroup_tex': 'C_{217}:C_6', 'supersolvable': True, 'sylow': 0}
id: 71243920
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 651, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 651, 'label': '1302.10.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '651.4', 'subgroup_hash': 4, 'subgroup_order': 651, 'subgroup_tex': 'C_{217}:C_3', 'supersolvable': True, 'sylow': 0}
id: 71243921
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 31, 'characteristic': True, 'core_order': 434, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 434, 'label': '1302.10.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '434.1', 'subgroup_hash': 1, 'subgroup_order': 434, 'subgroup_tex': 'D_7\\times C_{31}', 'supersolvable': True, 'sylow': 0}
id: 71243922
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 217, 'characteristic': True, 'core_order': 217, 'counter': 4, 'cyclic': True, 'direct': False, 'hall': 217, 'label': '1302.10.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '217.1', 'subgroup_hash': 1, 'subgroup_order': 217, 'subgroup_tex': 'C_{217}', 'supersolvable': True, 'sylow': 0}
id: 71243923
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 31, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 186, 'label': '1302.10.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '186.2', 'subgroup_hash': 2, 'subgroup_order': 186, 'subgroup_tex': 'C_{31}:C_6', 'supersolvable': True, 'sylow': 0}
id: 71243924
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 31, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 93, 'label': '1302.10.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '93.1', 'subgroup_hash': 1, 'subgroup_order': 93, 'subgroup_tex': 'C_{31}:C_3', 'supersolvable': True, 'sylow': 0}
id: 71243925
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 62, 'characteristic': False, 'core_order': 31, 'counter': 7, 'cyclic': True, 'direct': None, 'hall': 62, 'label': '1302.10.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '62.2', 'subgroup_hash': 2, 'subgroup_order': 62, 'subgroup_tex': 'C_{62}', 'supersolvable': True, 'sylow': 0}
id: 71243926
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 14, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 42, 'label': '1302.10.31.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '31.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 31, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
id: 71243927
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 434, 'characteristic': True, 'core_order': 31, 'counter': 9, 'cyclic': True, 'direct': False, 'hall': 31, 'label': '1302.10.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '42.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_7', 'simple': True, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '31.1', 'subgroup_hash': 1, 'subgroup_order': 31, 'subgroup_tex': 'C_{31}', 'supersolvable': True, 'sylow': 31}
id: 71243913
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 7, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 21, 'label': '1302.10.62.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '62.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 62, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
id: 71243914
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 31, 'characteristic': True, 'core_order': 14, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 14, 'label': '1302.10.93.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '93.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '93.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 93, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{31}:C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 71243915
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 217, 'characteristic': True, 'core_order': 7, 'counter': 12, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1302.10.186.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '186.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '186.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 186, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{31}:C_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
id: 71243916
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': True, 'direct': None, 'hall': 6, 'label': '1302.10.217.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '217.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 217, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 71243917
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '1302.10.434.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '434.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 434, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
id: 71243918
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 186, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '1302.10.651.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '651.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 651, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 2}
id: 71243919
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1302.10', 'ambient_counter': 10, 'ambient_order': 1302, 'ambient_tex': 'C_{217}:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 1302, 'characteristic': True, 'core_order': 1, 'counter': 16, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1302.10.1302.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1302.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1302.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1302, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{217}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

Column	Type
ambient	text
aut_centralizer_order	numeric
aut_label	text
aut_quo_index	numeric
aut_stab_index	numeric
aut_weyl_group	text
aut_weyl_index	numeric
centralizer	text
complements	text[]
conjugacy_class_count	numeric
contained_in	text[]
contains	text[]
core	text
coset_action_label	text
count	numeric
diagramx	smallint[]
generators	numeric[]
label	text
mobius_quo	bigint
mobius_sub	bigint
normal_closure	text
normal_contained_in	text[]
normal_contains	text[]
normalizer	text
old_label	text
projective_image	text
quotient_action_image	text
quotient_action_kernel	text
quotient_action_kernel_order	numeric
quotient_fusion	jsonb
short_label	text
subgroup_fusion	integer[]
weyl_group	text

gps_subgroup_data • Show schema

id: 71243912
{'ambient': '1302.10', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1302.a1.a1', 'complements': ['1302.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '7.a1.a1', '31.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2940, 4849, 2765, 5373, 4815, 4672, 4815, 4672], 'generators': [3, 2, 42, 930], 'label': '1302.10.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1302.10'}
id: 71243913
{'ambient': '1302.10', 'aut_centralizer_order': 30, 'aut_label': '62.a1', 'aut_quo_index': None, 'aut_stab_index': 31, 'aut_weyl_group': '42.1', 'aut_weyl_index': 930, 'centralizer': '1302.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '31.a1.a1'], 'contains': ['186.a1.a1', '434.a1.a1'], 'core': '186.a1.a1', 'coset_action_label': None, 'count': 31, 'diagramx': [3463, -1, 3463, -1, 2500, -1, 2500, -1], 'generators': [2, 930], 'label': '1302.10.62.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '31.a1.a1', 'old_label': '62.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '62.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 71243914
{'ambient': '1302.10', 'aut_centralizer_order': 930, 'aut_label': '93.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 930, 'centralizer': '42.a1.a1', 'complements': ['14.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '31.a1.a1'], 'contains': ['186.a1.a1', '651.a1.a1'], 'core': '93.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1450, 2765, 1450, 8139, 4019, 7336, 4019, 7336], 'generators': [3, 930], 'label': '1302.10.93.a1.a1', 'mobius_quo': 0, 'mobius_sub': 31, 'normal_closure': '93.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['186.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '93.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': '3.1', 'quotient_action_kernel': '31.1', 'quotient_action_kernel_order': 31, 'quotient_fusion': None, 'short_label': '93.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 71243915
{'ambient': '1302.10', 'aut_centralizer_order': 6510, 'aut_label': '186.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 6510, 'centralizer': '6.a1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '62.a1.a1', '93.a1.a1'], 'contains': ['1302.a1.a1'], 'core': '186.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1508, 4849, 1780, 5213, 2815, 7153, 2815, 7153], 'generators': [930], 'label': '1302.10.186.a1.a1', 'mobius_quo': -1, 'mobius_sub': -31, 'normal_closure': '186.a1.a1', 'normal_contained_in': ['6.a1.a1', '93.a1.a1'], 'normal_contains': ['1302.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '186.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': '6.2', 'quotient_action_kernel': '31.1', 'quotient_action_kernel_order': 31, 'quotient_fusion': None, 'short_label': '186.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 71243916
{'ambient': '1302.10', 'aut_centralizer_order': 180, 'aut_label': '217.a1', 'aut_quo_index': None, 'aut_stab_index': 217, 'aut_weyl_group': '1.1', 'aut_weyl_index': 39060, 'centralizer': '217.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '31.a1.a1'], 'contains': ['434.a1.a1', '651.a1.a1'], 'core': '1302.a1.a1', 'coset_action_label': None, 'count': 217, 'diagramx': [4701, -1, 4817, -1, 9204, -1, 9204, -1], 'generators': [3, 2], 'label': '1302.10.217.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '217.a1.a1', 'old_label': '217.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '217.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71243917
{'ambient': '1302.10', 'aut_centralizer_order': 180, 'aut_label': '434.a1', 'aut_quo_index': None, 'aut_stab_index': 217, 'aut_weyl_group': '1.1', 'aut_weyl_index': 39060, 'centralizer': '217.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '62.a1.a1', '217.a1.a1'], 'contains': ['1302.a1.a1'], 'core': '1302.a1.a1', 'coset_action_label': None, 'count': 217, 'diagramx': [5571, -1, 5725, -1, 5944, -1, 5944, -1], 'generators': [2], 'label': '1302.10.434.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '217.a1.a1', 'old_label': '434.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '434.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71243918
{'ambient': '1302.10', 'aut_centralizer_order': 5580, 'aut_label': '651.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 39060, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1.a1', '93.a1.a1', '217.a1.a1'], 'contains': ['1302.a1.a1'], 'core': '1302.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3791, -1, 3907, -1, 7574, -1, 7574, -1], 'generators': [3], 'label': '1302.10.651.a1.a1', 'mobius_quo': None, 'mobius_sub': -31, 'normal_closure': '93.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '651.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '651.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71243919
{'ambient': '1302.10', 'aut_centralizer_order': None, 'aut_label': '1302.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': ['42.a1.a1', '186.a1.a1', '434.a1.a1', '651.a1.a1'], 'contains': [], 'core': '1302.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4894, 5985, 5010, 3670, 5204, 5693, 5204, 5693], 'generators': [], 'label': '1302.10.1302.a1.a1', 'mobius_quo': 1, 'mobius_sub': 217, 'normal_closure': '1302.a1.a1', 'normal_contained_in': ['42.a1.a1', '186.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1302.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1302.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71243920
{'ambient': '1302.10', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '1302.a1.a1', 'complements': ['651.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '14.a1.a1', '62.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3733, 6364, 3733, 3032, 1019, 2007, 1019, 2007], 'generators': [2, 930, 42], 'label': '1302.10.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1302.10'}
id: 71243921
{'ambient': '1302.10', 'aut_centralizer_order': 31, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1260.75', 'aut_weyl_index': 31, 'centralizer': '42.a1.a1', 'complements': ['434.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '21.a1.a1', '93.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1412, 2765, 1412, 8139, 3722, 7336, 3722, 7336], 'generators': [3, 42, 930], 'label': '1302.10.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '93.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 71243922
{'ambient': '1302.10', 'aut_centralizer_order': 217, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '180.37', 'aut_weyl_index': 217, 'centralizer': '6.a1.a1', 'complements': ['217.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['42.a1.a1', '186.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2785, 5985, 2785, 3618, 741, 4233, 741, 4233], 'generators': [930, 42], 'label': '1302.10.6.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['42.a1.a1', '186.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 71243923
{'ambient': '1302.10', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '930.1', 'aut_weyl_index': 42, 'centralizer': '651.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '21.a1.a1', '217.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6344, -1, 6344, -1, 8370, -1, 8370, -1], 'generators': [3, 2, 42], 'label': '1302.10.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '93.1'}
id: 71243924
{'ambient': '1302.10', 'aut_centralizer_order': 6, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '930.1', 'aut_weyl_index': 42, 'centralizer': '651.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '434.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8588, -1, 8588, -1, 5796, -1, 5796, -1], 'generators': [2, 42], 'label': '1302.10.14.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '93.1'}
id: 71243925
{'ambient': '1302.10', 'aut_centralizer_order': 186, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '30.4', 'aut_weyl_index': 1302, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '651.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4584, -1, 4759, -1, 7722, -1, 7722, -1], 'generators': [3, 42], 'label': '1302.10.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 71243926
{'ambient': '1302.10', 'aut_centralizer_order': 30, 'aut_label': '31.a1', 'aut_quo_index': None, 'aut_stab_index': 31, 'aut_weyl_group': '42.1', 'aut_weyl_index': 930, 'centralizer': '1302.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['62.a1.a1', '93.a1.a1', '217.a1.a1'], 'core': '93.a1.a1', 'coset_action_label': None, 'count': 31, 'diagramx': [2011, -1, 2011, -1, 5907, -1, 5907, -1], 'generators': [3, 930, 2], 'label': '1302.10.31.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '31.a1.a1', 'old_label': '31.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '31.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 71243927
{'ambient': '1302.10', 'aut_centralizer_order': 1302, 'aut_label': '42.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '30.4', 'aut_weyl_index': 1302, 'centralizer': '3.a1.a1', 'complements': ['31.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['1302.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5880, 7235, 6055, 1861, 4463, 4233, 4463, 4233], 'generators': [42], 'label': '1302.10.42.a1.a1', 'mobius_quo': -1, 'mobius_sub': -7, 'normal_closure': '42.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['1302.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '1302.10', 'quotient_action_image': '3.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.