LMFDB - Abstract group data

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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': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [6, 2, 2, 7, 2, 2, 6, 2, 4, 2], 'aut_gens': [[1, 2, 4, 16], [125, 2, 121, 208], [9, 2, 4, 208], [1, 114, 124, 208], [1, 34, 4, 16], [1, 2, 12, 208], [1, 2, 4, 216], [1, 2, 4, 48], [1, 10, 4, 208], [5, 10, 4, 208], [1, 114, 4, 208]], 'aut_group': '32256.bi', 'aut_hash': 5280945712516171064, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 19, 'aut_perms': [1466077363400264, 1466077363395409, 1466077363027282, 7180527132979200, 1466077363402396, 1466077450499778, 1782366430884480, 1466077323110400, 1466077363411780, 1466077363027200], 'aut_phi_ratio': 336.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 7, 4, 1], [4, 2, 6, 1], [4, 14, 6, 1], [7, 2, 3, 1], [14, 2, 3, 1], [14, 2, 6, 1], [28, 4, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\wr D_6.F_7', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '252.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 252, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 7, 4], [4, 2, 6], [4, 14, 6], [7, 2, 3], [14, 2, 9], [28, 4, 18]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '56.12', 'commutator_count': 1, 'commutator_label': '14.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 181, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['14.1', 1], ['2.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 7, 1, 4], [4, 2, 1, 6], [4, 14, 1, 6], [7, 2, 3, 1], [14, 2, 3, 3], [28, 4, 3, 6]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 23940, 'exponent': 28, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '112.42', 'hash': 181, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 2, 2, 7], 'inner_gens': [[1, 2, 12, 16], [1, 2, 4, 208], [9, 2, 4, 16], [1, 34, 4, 16]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 56, 'inner_split': False, 'inner_tex': 'C_2\\times D_{14}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 28], [4, 6]], 'label': '224.181', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'Q8*D14', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 10, 'number_conjugacy_classes': 50, 'number_divisions': 30, 'number_normal_subgroups': 97, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 156, 'number_subgroups': 510, 'old_label': None, 'order': 224, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 31], [4, 96], [7, 6], [14, 18], [28, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 6, 2, 4, 6], 'outer_gen_pows': [1, 0, 0, 0, 0], 'outer_gens': [[1, 2, 125, 16], [5, 2, 113, 24], [121, 2, 4, 16], [1, 114, 4, 24], [1, 2, 116, 80]], 'outer_group': '576.8437', 'outer_hash': 8437, 'outer_nilpotent': False, 'outer_order': 576, 'outer_permdeg': 11, 'outer_perms': [41064, 403224, 11652480, 1704, 3669123], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,\\mathbb{Z}/4):C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 4], [6, 8], [12, 2]], 'representations': {'PC': {'code': 138695379422028684100421, 'gens': [1, 2, 3, 5], 'pres': [6, -2, -2, -2, -2, -2, -7, 48, 218, 50, 3130, 88, 3467]}, 'GLZN': {'d': 2, 'p': 21, 'gens': [9325, 120406, 80557, 74096, 77323, 185354]}, 'Perm': {'d': 17, 'gens': [40447, 40320, 23906015481600, 45968909051520, 68436399225600, 973]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_8\\times D_{14}', 'transitive_degree': 112, '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: 98194882
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 181, 'group_order': 224, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 98194893
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 181, 'group_order': 224, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 8, 'size': 1}
id: 98194904
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 181, 'group_order': 224, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 112, 'size': 1}
id: 98194915
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 181, 'group_order': 224, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 120, 'size': 1}
id: 98194926
{'aut_label': '2D', 'centralizer': '7.a1', 'counter': 5, 'group_counter': 181, 'group_order': 224, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 2, 'size': 7}
id: 98194928
{'aut_label': '2D', 'centralizer': '7.a1', 'counter': 6, 'group_counter': 181, 'group_order': 224, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 18, 'size': 7}
id: 98194929
{'aut_label': '2D', 'centralizer': '7.a1', 'counter': 7, 'group_counter': 181, 'group_order': 224, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 10, 'size': 7}
id: 98194930
{'aut_label': '2D', 'centralizer': '7.a1', 'counter': 8, 'group_counter': 181, 'group_order': 224, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 26, 'size': 7}
id: 98194931
{'aut_label': '4A', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 181, 'group_order': 224, 'label': '4A', 'order': 4, 'powers': [2, 9, 9], 'representative': 12, 'size': 2}
id: 98194883
{'aut_label': '4A', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 181, 'group_order': 224, 'label': '4B', 'order': 4, 'powers': [2, 10, 10], 'representative': 124, 'size': 2}
id: 98194884
{'aut_label': '4A', 'centralizer': '2.a1', 'counter': 11, 'group_counter': 181, 'group_order': 224, 'label': '4C', 'order': 4, 'powers': [2, 11, 11], 'representative': 9, 'size': 2}
id: 98194885
{'aut_label': '4A', 'centralizer': '2.a1', 'counter': 12, 'group_counter': 181, 'group_order': 224, 'label': '4D', 'order': 4, 'powers': [2, 12, 12], 'representative': 121, 'size': 2}
id: 98194886
{'aut_label': '4A', 'centralizer': '2.a1', 'counter': 13, 'group_counter': 181, 'group_order': 224, 'label': '4E', 'order': 4, 'powers': [2, 13, 13], 'representative': 13, 'size': 2}
id: 98194887
{'aut_label': '4A', 'centralizer': '2.a1', 'counter': 14, 'group_counter': 181, 'group_order': 224, 'label': '4F', 'order': 4, 'powers': [2, 14, 14], 'representative': 125, 'size': 2}
id: 98194888
{'aut_label': '4G', 'centralizer': '14.b1', 'counter': 15, 'group_counter': 181, 'group_order': 224, 'label': '4G', 'order': 4, 'powers': [2, 15, 15], 'representative': 6, 'size': 14}
id: 98194889
{'aut_label': '4G', 'centralizer': '14.b1', 'counter': 16, 'group_counter': 181, 'group_order': 224, 'label': '4H', 'order': 4, 'powers': [2, 16, 16], 'representative': 3, 'size': 14}
id: 98194890
{'aut_label': '4G', 'centralizer': '14.b1', 'counter': 17, 'group_counter': 181, 'group_order': 224, 'label': '4I', 'order': 4, 'powers': [2, 17, 17], 'representative': 22, 'size': 14}
id: 98194891
{'aut_label': '4G', 'centralizer': '14.b1', 'counter': 18, 'group_counter': 181, 'group_order': 224, 'label': '4J', 'order': 4, 'powers': [2, 18, 18], 'representative': 19, 'size': 14}
id: 98194892
{'aut_label': '4G', 'centralizer': '14.b1', 'counter': 19, 'group_counter': 181, 'group_order': 224, 'label': '4K', 'order': 4, 'powers': [2, 19, 19], 'representative': 7, 'size': 14}
id: 98194894
{'aut_label': '4G', 'centralizer': '14.b1', 'counter': 20, 'group_counter': 181, 'group_order': 224, 'label': '4L', 'order': 4, 'powers': [2, 20, 20], 'representative': 23, 'size': 14}
id: 98194895
{'aut_label': '7A1', 'centralizer': '2.c1', 'counter': 21, 'group_counter': 181, 'group_order': 224, 'label': '7A1', 'order': 7, 'powers': [22, 23, 1], 'representative': 32, 'size': 2}
id: 98194896
{'aut_label': '7A1', 'centralizer': '2.c1', 'counter': 22, 'group_counter': 181, 'group_order': 224, 'label': '7A2', 'order': 7, 'powers': [23, 21, 1], 'representative': 64, 'size': 2}
id: 98194897
{'aut_label': '7A1', 'centralizer': '2.c1', 'counter': 23, 'group_counter': 181, 'group_order': 224, 'label': '7A3', 'order': 7, 'powers': [21, 22, 1], 'representative': 96, 'size': 2}
id: 98194898
{'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 24, 'group_counter': 181, 'group_order': 224, 'label': '14A1', 'order': 14, 'powers': [21, 25, 3], 'representative': 16, 'size': 2}
id: 98194899
{'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 25, 'group_counter': 181, 'group_order': 224, 'label': '14A3', 'order': 14, 'powers': [23, 26, 3], 'representative': 48, 'size': 2}
id: 98194900
{'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 26, 'group_counter': 181, 'group_order': 224, 'label': '14A5', 'order': 14, 'powers': [22, 24, 3], 'representative': 80, 'size': 2}
id: 98194901
{'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 27, 'group_counter': 181, 'group_order': 224, 'label': '14B1', 'order': 14, 'powers': [21, 28, 4], 'representative': 24, 'size': 2}
id: 98194902
{'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 28, 'group_counter': 181, 'group_order': 224, 'label': '14B3', 'order': 14, 'powers': [23, 29, 4], 'representative': 56, 'size': 2}
id: 98194903
{'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 29, 'group_counter': 181, 'group_order': 224, 'label': '14B5', 'order': 14, 'powers': [22, 27, 4], 'representative': 88, 'size': 2}
id: 98194905
{'aut_label': '14C1', 'centralizer': '2.c1', 'counter': 30, 'group_counter': 181, 'group_order': 224, 'label': '14C1', 'order': 14, 'powers': [23, 31, 2], 'representative': 72, 'size': 2}
id: 98194906
{'aut_label': '14C1', 'centralizer': '2.c1', 'counter': 31, 'group_counter': 181, 'group_order': 224, 'label': '14C3', 'order': 14, 'powers': [22, 32, 2], 'representative': 200, 'size': 2}
id: 98194907
{'aut_label': '14C1', 'centralizer': '2.c1', 'counter': 32, 'group_counter': 181, 'group_order': 224, 'label': '14C5', 'order': 14, 'powers': [21, 30, 2], 'representative': 104, 'size': 2}
id: 98194908
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 33, 'group_counter': 181, 'group_order': 224, 'label': '28A1', 'order': 28, 'powers': [30, 34, 9], 'representative': 36, 'size': 4}
id: 98194909
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 34, 'group_counter': 181, 'group_order': 224, 'label': '28A3', 'order': 28, 'powers': [31, 35, 9], 'representative': 100, 'size': 4}
id: 98194910
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 35, 'group_counter': 181, 'group_order': 224, 'label': '28A5', 'order': 28, 'powers': [32, 33, 9], 'representative': 68, 'size': 4}
id: 98194911
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 36, 'group_counter': 181, 'group_order': 224, 'label': '28B1', 'order': 28, 'powers': [31, 37, 10], 'representative': 20, 'size': 4}
id: 98194912
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 37, 'group_counter': 181, 'group_order': 224, 'label': '28B3', 'order': 28, 'powers': [32, 38, 10], 'representative': 52, 'size': 4}
id: 98194913
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 38, 'group_counter': 181, 'group_order': 224, 'label': '28B5', 'order': 28, 'powers': [30, 36, 10], 'representative': 84, 'size': 4}
id: 98194914
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 39, 'group_counter': 181, 'group_order': 224, 'label': '28C1', 'order': 28, 'powers': [30, 40, 11], 'representative': 33, 'size': 4}
id: 98194916
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 40, 'group_counter': 181, 'group_order': 224, 'label': '28C3', 'order': 28, 'powers': [31, 41, 11], 'representative': 97, 'size': 4}
id: 98194917
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 41, 'group_counter': 181, 'group_order': 224, 'label': '28C5', 'order': 28, 'powers': [32, 39, 11], 'representative': 65, 'size': 4}
id: 98194918
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 42, 'group_counter': 181, 'group_order': 224, 'label': '28D1', 'order': 28, 'powers': [31, 43, 12], 'representative': 17, 'size': 4}
id: 98194919
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 43, 'group_counter': 181, 'group_order': 224, 'label': '28D3', 'order': 28, 'powers': [32, 44, 12], 'representative': 49, 'size': 4}
id: 98194920
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 44, 'group_counter': 181, 'group_order': 224, 'label': '28D5', 'order': 28, 'powers': [30, 42, 12], 'representative': 81, 'size': 4}
id: 98194921
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 45, 'group_counter': 181, 'group_order': 224, 'label': '28E1', 'order': 28, 'powers': [30, 46, 13], 'representative': 37, 'size': 4}
id: 98194922
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 46, 'group_counter': 181, 'group_order': 224, 'label': '28E3', 'order': 28, 'powers': [31, 47, 13], 'representative': 101, 'size': 4}
id: 98194923
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 47, 'group_counter': 181, 'group_order': 224, 'label': '28E5', 'order': 28, 'powers': [32, 45, 13], 'representative': 69, 'size': 4}
id: 98194924
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 48, 'group_counter': 181, 'group_order': 224, 'label': '28F1', 'order': 28, 'powers': [31, 49, 14], 'representative': 21, 'size': 4}
id: 98194925
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 49, 'group_counter': 181, 'group_order': 224, 'label': '28F3', 'order': 28, 'powers': [32, 50, 14], 'representative': 53, 'size': 4}
id: 98194927
{'aut_label': '28A1', 'centralizer': '4.b1', 'counter': 50, 'group_counter': 181, 'group_order': 224, 'label': '28F5', 'order': 28, 'powers': [30, 48, 14], 'representative': 85, 'size': 4}

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: 269397
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1a', '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], 'schur_index': 1}
id: 269408
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1b', '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], 'schur_index': 1}
id: 269419
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1c', '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], 'schur_index': 1}
id: 269421
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1d', '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], 'schur_index': 1}
id: 269422
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1e', '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], 'schur_index': 1}
id: 269423
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1f', '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], 'schur_index': 1}
id: 269424
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1g', '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], 'schur_index': 1}
id: 269425
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1h', '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], 'schur_index': 1}
id: 269426
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1i', '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], 'schur_index': 1}
id: 269398
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1j', '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], 'schur_index': 1}
id: 269399
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1k', '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], 'schur_index': 1}
id: 269400
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1l', '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], 'schur_index': 1}
id: 269401
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1m', '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], 'schur_index': 1}
id: 269402
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1n', '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], 'schur_index': 1}
id: 269403
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1o', '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], 'schur_index': 1}
id: 269404
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.1p', '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], 'schur_index': 1}
id: 269405
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2a', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 269406
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2b', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 269407
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2c', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 269409
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2d', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 269410
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2e', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 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: 269411
{'cdim': 2, 'counter': 22, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2f', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, 0, 0, -6, 6, -6, 6, 6, -6, 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: 269412
{'cdim': 2, 'counter': 23, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2g', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, 0, 0, -6, 6, 6, -6, -6, 6, 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: 269413
{'cdim': 2, 'counter': 24, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2h', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, 0, 0, 6, -6, -6, 6, -6, 6, 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: 269414
{'cdim': 2, 'counter': 25, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2i', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, 0, 0, 6, -6, 6, -6, 6, -6, 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: 269415
{'cdim': 2, 'counter': 26, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2j', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, -6, -6, -6, -6, 6, 6, 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: 269416
{'cdim': 2, 'counter': 27, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2k', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, -6, -6, 6, 6, -6, -6, 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: 269417
{'cdim': 2, 'counter': 28, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.2l', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, 6, 6, -6, -6, -6, -6, 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: 269418
{'cdim': 4, 'counter': 29, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.4a', 'multiplicity': 3, 'nt': [56, 0], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 269420
{'cdim': 4, 'counter': 30, 'faithful': False, 'group': '224.181', 'group_order': 224, 'image': None, 'label': '224.181.4b', 'multiplicity': 3, 'nt': [56, 0], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}

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: 387596
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 224, 'label': '224.181.1a', '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]]]}
id: 387607
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 112, 'label': '224.181.1b', '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]]]}
id: 387618
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 112, 'label': '224.181.1c', '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]]]}
id: 387629
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 112, 'label': '224.181.1d', '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]]]}
id: 387640
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id: 387642
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id: 387643
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id: 387644
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id: 387645
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 112, 'label': '224.181.1i', '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]]]}
id: 387597
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 112, 'label': '224.181.1j', '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]]]}
id: 387598
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 112, 'label': '224.181.1k', '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]]]}
id: 387599
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 112, 'label': '224.181.1l', '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]]]}
id: 387600
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 112, 'label': '224.181.1m', '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]]]}
id: 387601
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 112, 'label': '224.181.1n', '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]]]}
id: 387602
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 112, 'label': '224.181.1o', '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]]]}
id: 387603
{'center': '1.a1', 'center_index': 1, 'center_order': 224, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 112, 'label': '224.181.1p', '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]]]}
id: 387604
{'center': '4.a1', 'center_index': 4, 'center_order': 56, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.e1', 'kernel_order': 28, 'label': '224.181.2a', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387605
{'center': '4.a1', 'center_index': 4, 'center_order': 56, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.e1', 'kernel_order': 28, 'label': '224.181.2b', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387606
{'center': '4.a1', 'center_index': 4, 'center_order': 56, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.e1', 'kernel_order': 28, 'label': '224.181.2c', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387608
{'center': '4.a1', 'center_index': 4, 'center_order': 56, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.e1', 'kernel_order': 28, 'label': '224.181.2d', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387609
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 21, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1', 'kernel_order': 16, 'label': '224.181.2e1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
id: 387610
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 22, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1', 'kernel_order': 16, 'label': '224.181.2e2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
id: 387611
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1', 'kernel_order': 16, 'label': '224.181.2e3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
id: 387612
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2f1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]]]}
id: 387613
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 25, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2f2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]]]}
id: 387614
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 26, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2f3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]]]}
id: 387615
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 27, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2g1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
id: 387616
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 28, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2g2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]]]}
id: 387617
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 29, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2g3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
id: 387619
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2h1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]]]}
id: 387620
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2h2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]]]}
id: 387621
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2h3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]]]}
id: 387622
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 33, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2i1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
id: 387623
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 34, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2i2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
id: 387624
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 35, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 8, 'label': '224.181.2i3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
id: 387625
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 36, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2j1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]]]}
id: 387626
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2j2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]]]}
id: 387627
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 38, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2j3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]]]}
id: 387628
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 39, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2k1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
id: 387630
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 40, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2k2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]]]}
id: 387631
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 41, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2k3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
id: 387632
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 42, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2l1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]]]}
id: 387633
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 43, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2l2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]]]}
id: 387634
{'center': '14.a1', 'center_index': 14, 'center_order': 16, 'counter': 44, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 8, 'label': '224.181.2l3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]]]}
id: 387635
{'center': '56.a1', 'center_index': 56, 'center_order': 4, 'counter': 45, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '112.33', 'image_order': 112, 'indicator': -1, 'kernel': '112.b1', 'kernel_order': 2, 'label': '224.181.4a1', 'nt': [56, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387636
{'center': '56.a1', 'center_index': 56, 'center_order': 4, 'counter': 46, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '112.33', 'image_order': 112, 'indicator': -1, 'kernel': '112.b1', 'kernel_order': 2, 'label': '224.181.4a2', 'nt': [56, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387637
{'center': '56.a1', 'center_index': 56, 'center_order': 4, 'counter': 47, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '112.33', 'image_order': 112, 'indicator': -1, 'kernel': '112.b1', 'kernel_order': 2, 'label': '224.181.4a3', 'nt': [56, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387638
{'center': '56.a1', 'center_index': 56, 'center_order': 4, 'counter': 48, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '112.33', 'image_order': 112, 'indicator': -1, 'kernel': '112.b1', 'kernel_order': 2, 'label': '224.181.4b1', 'nt': [56, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387639
{'center': '56.a1', 'center_index': 56, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '112.33', 'image_order': 112, 'indicator': -1, 'kernel': '112.b1', 'kernel_order': 2, 'label': '224.181.4b2', 'nt': [56, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 387641
{'center': '56.a1', 'center_index': 56, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.181', 'group_counter': 181, 'group_order': 224, 'image': None, 'image_isoclass': '112.33', 'image_order': 112, 'indicator': -1, 'kernel': '112.b1', 'kernel_order': 2, 'label': '224.181.4b3', 'nt': [56, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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: 20967613
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 224, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 14, 'label': '224.181.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '224.181', 'subgroup_hash': 181, 'subgroup_order': 224, 'subgroup_tex': 'Q_8\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967624
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.28', 'subgroup_hash': 28, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967635
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967646
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 112, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.39', 'subgroup_hash': 39, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967648
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.181.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, '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': '112.33', 'subgroup_hash': 33, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 20967649
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': True, 'core_order': 56, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967650
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 20967651
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
id: 20967652
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 20967614
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967615
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 56, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.10', 'subgroup_hash': 10, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967616
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '224.181.7.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7.a1', 'outer_equivalence': True, '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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 2}
id: 20967617
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 28, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967618
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967619
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 28, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.181.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 20967620
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
id: 20967621
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 17, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.181.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967622
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 56, 'characteristic': True, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.181.14.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967623
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.14.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.b1', 'outer_equivalence': True, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20967625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.14.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1', 'outer_equivalence': True, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967626
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.14.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.d1', 'outer_equivalence': True, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967627
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 14, 'counter': 22, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.181.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967628
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 23, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.181.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 20967629
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 14, 'counter': 24, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.181.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', '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: 20967630
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.28.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20967631
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.181.28.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967632
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.28.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.c1', 'outer_equivalence': True, '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': 28, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 20967633
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.28.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1', 'outer_equivalence': True, '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': 28, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20967634
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.28.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1', 'outer_equivalence': True, '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': 28, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20967636
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.28.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.f1', 'outer_equivalence': True, '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': 28, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 20967637
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 7, 'counter': 31, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '224.181.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times Q_8', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
id: 20967638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 4, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.181.56.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 20967639
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 33, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.181.56.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 20967640
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.56.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.c1', 'outer_equivalence': True, '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': 56, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 20967641
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '224.181.56.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1', 'outer_equivalence': True, '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': 56, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 20967642
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.181.56.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1', 'outer_equivalence': True, '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': 56, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 20967643
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 2, 'counter': 37, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.181.112.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '112.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '112.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_{14}', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 20967644
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '224.181.112.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '112.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '112.33', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 33, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times D_7', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 20967645
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '224.181.112.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1', 'outer_equivalence': True, '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': 112, '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': 0}
id: 20967647
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.181', 'ambient_counter': 181, 'ambient_order': 224, 'ambient_tex': 'Q_8\\times D_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 1, 'counter': 40, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '224.181.224.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '224.181', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 181, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C6'], '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: 20967633
{'ambient': '224.181', 'aut_centralizer_order': 192, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '14.b1', '14.c1'], 'contains': ['56.a1', '56.d1'], 'core': '56.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [4296, -1, 6058, -1], 'generators': [6, 112], 'label': '224.181.28.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.d1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967632
{'ambient': '224.181', 'aut_centralizer_order': 576, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '14.b1'], 'contains': ['56.a1', '56.c1', '56.e1'], 'core': '56.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2146, -1, 8558, -1], 'generators': [2, 8, 112], 'label': '224.181.28.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.c1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967613
{'ambient': '224.181', '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': '56.a1', 'complements': ['224.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '7.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7954, 6611, 3723, 6023], 'generators': [1, 32, 4, 112, 2, 8], 'label': '224.181.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 20967614
{'ambient': '224.181', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 12, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '56.a1', 'complements': ['56.e1'], 'conjugacy_class_count': 12, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.c1', '8.d1', '28.f1'], 'core': '4.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [7731, 7466, 4010, 6803], 'generators': [3, 8, 32, 124], 'label': '224.181.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '112.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 20967615
{'ambient': '224.181', 'aut_centralizer_order': 56, 'aut_label': '4.f1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '144.188', 'aut_weyl_index': 224, 'centralizer': '8.a1', 'complements': ['56.e1'], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '2.d1'], 'contains': ['8.c1', '28.b1'], 'core': '4.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [9305, 8761, 1346, 7984], 'generators': [121, 32, 8, 4], 'label': '224.181.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.c1', '2.d1'], 'normal_contains': ['8.c1', '28.b1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '112.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 20967616
{'ambient': '224.181', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '768.1087581', 'aut_weyl_index': 42, 'centralizer': '28.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['14.a1', '14.b1', '14.c1', '14.d1'], 'core': '14.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9387, -1, 2709, -1], 'generators': [1, 2, 4, 112], 'label': '224.181.7.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '7.a1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967617
{'ambient': '224.181', 'aut_centralizer_order': 2688, 'aut_label': '8.a1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '16.b1', '56.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2739, 3210, 7716, 3007], 'generators': [8, 32, 112], 'label': '224.181.8.a1', 'mobius_quo': -2, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '16.b1', '56.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '56.12', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967618
{'ambient': '224.181', 'aut_centralizer_order': 192, 'aut_label': '8.b1', 'aut_quo_index': 7, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '14.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.d1'], 'contains': ['16.a1', '16.c1', '56.c1'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1702, 1790, 9147, 1714], 'generators': [2, 32, 8], 'label': '224.181.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.d1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 20967619
{'ambient': '224.181', 'aut_centralizer_order': 448, 'aut_label': '8.c1', 'aut_quo_index': 42, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '4.d1', '4.e1', '4.f1'], 'contains': ['16.a1', '56.b1'], 'core': '8.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [6693, 6869, 4360, 5326], 'generators': [124, 8, 32], 'label': '224.181.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.d1', '4.e1', '4.f1'], 'normal_contains': ['16.a1', '56.b1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '112.42', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967620
{'ambient': '224.181', 'aut_centralizer_order': 64, 'aut_label': '8.d1', 'aut_quo_index': 21, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '28.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '56.d1'], 'core': '8.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [4107, 4651, 6839, 4320], 'generators': [6, 32, 8], 'label': '224.181.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 20967621
{'ambient': '224.181', 'aut_centralizer_order': 96, 'aut_label': '8.e1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '14.a1', 'complements': ['28.b1', '28.f1'], 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['16.b1', '16.c1', '56.e1'], 'core': '8.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [292, 788, 9757, 800], 'generators': [2, 32, 112], 'label': '224.181.8.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '112.33', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 20967622
{'ambient': '224.181', 'aut_centralizer_order': 168, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.955', 'aut_weyl_index': 168, 'centralizer': '4.a1', 'complements': ['16.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '7.a1'], 'contains': ['28.a1', '28.b1'], 'core': '14.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9732, 9212, 408, 9389], 'generators': [1, 4, 112], 'label': '224.181.14.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1', 'normal_contained_in': ['2.c1'], 'normal_contains': ['28.a1', '28.b1'], 'normalizer': '1.a1', 'old_label': '14.a1', 'projective_image': '56.12', 'quotient_action_image': '1.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '14.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967623
{'ambient': '224.181', 'aut_centralizer_order': 48, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.27', 'aut_weyl_index': 1008, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '7.a1'], 'contains': ['28.a1', '28.c1', '28.d1', '28.e1'], 'core': '28.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [4700, -1, 5983, -1], 'generators': [2, 4, 112], 'label': '224.181.14.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.b1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967624
{'ambient': '224.181', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '1344.6612', 'aut_weyl_index': 24, 'centralizer': '28.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1', '14.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4931, 3626, 6106, 3304], 'generators': [2, 112, 8, 4, 32], 'label': '224.181.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 20967625
{'ambient': '224.181', 'aut_centralizer_order': 24, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 504, 'centralizer': '28.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '7.a1'], 'contains': ['28.a1', '28.d1', '28.f1'], 'core': '28.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7155, -1, 3223, -1], 'generators': [3, 4, 112], 'label': '224.181.14.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.c1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967626
{'ambient': '224.181', 'aut_centralizer_order': 12, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '48.48', 'aut_weyl_index': 672, 'centralizer': '28.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.d1', '7.a1'], 'contains': ['28.b1', '28.e1', '28.f1'], 'core': '28.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [8604, -1, 2284, -1], 'generators': [113, 2, 4], 'label': '224.181.14.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.d1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967627
{'ambient': '224.181', 'aut_centralizer_order': 5376, 'aut_label': '16.a1', 'aut_quo_index': 420, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['32.a1', '112.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2435, 3480, 7017, 3745], 'generators': [8, 32], 'label': '224.181.16.a1', 'mobius_quo': 1, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'normal_contains': ['32.a1', '112.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '112.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967628
{'ambient': '224.181', 'aut_centralizer_order': 2688, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.c1', 'complements': ['14.d1'], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.e1'], 'contains': ['32.a1', '112.b1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [992, 2489, 8181, 2842], 'generators': [112, 32], 'label': '224.181.16.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.e1'], 'normal_contains': ['32.a1', '112.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '112.33', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967629
{'ambient': '224.181', 'aut_centralizer_order': 192, 'aut_label': '16.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '14.a1', 'complements': ['14.a1', '14.c1', '14.d1'], 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.e1'], 'contains': ['32.a1', '112.c1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [268, 1587, 9291, 1714], 'generators': [2, 32], 'label': '224.181.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.e1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '224.181', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.12', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 20967630
{'ambient': '224.181', 'aut_centralizer_order': 1344, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '14.a1', '14.b1', '14.c1'], 'contains': ['56.a1', '56.b1'], 'core': '28.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6536, 6024, 3592, 6475], 'generators': [4, 112], 'label': '224.181.28.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1', 'normal_contained_in': ['4.b1', '14.a1'], 'normal_contains': ['56.a1', '56.b1'], 'normalizer': '1.a1', 'old_label': '28.a1', 'projective_image': '56.12', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967631
{'ambient': '224.181', 'aut_centralizer_order': 336, 'aut_label': '28.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1344, 'centralizer': '4.a1', 'complements': ['8.e1'], 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '14.a1', '14.d1'], 'contains': ['56.b1'], 'core': '28.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9503, 8221, 1818, 7984], 'generators': [113, 4], 'label': '224.181.28.b1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.b1', 'normal_contained_in': ['4.f1', '14.a1'], 'normal_contains': ['56.b1'], 'normalizer': '1.a1', 'old_label': '28.b1', 'projective_image': '112.42', 'quotient_action_image': '1.1', 'quotient_action_kernel': '28.3', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '28.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967634
{'ambient': '224.181', 'aut_centralizer_order': 96, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.d1', '14.b1', '14.d1'], 'contains': ['56.b1', '56.c1', '56.d1'], 'core': '56.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [5416, -1, 5127, -1], 'generators': [2, 116], 'label': '224.181.28.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.e1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967635
{'ambient': '224.181', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2688.dd', 'aut_weyl_index': 12, 'centralizer': '56.a1', 'complements': ['112.c1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.e1', '14.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6701, 5754, 4764, 5244], 'generators': [3, 112, 8, 4, 32], 'label': '224.181.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '56.12', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 20967636
{'ambient': '224.181', 'aut_centralizer_order': 48, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '28.c1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.e1', '14.c1', '14.d1'], 'contains': ['56.b1', '56.d1'], 'core': '56.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [7706, -1, 2880, -1], 'generators': [3, 116], 'label': '224.181.28.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.f1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967637
{'ambient': '224.181', 'aut_centralizer_order': 5376, 'aut_label': '32.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1'], 'contains': ['224.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [572, 2658, 8202, 2986], 'generators': [32], 'label': '224.181.32.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['224.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '224.181', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.12', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967638
{'ambient': '224.181', 'aut_centralizer_order': 16128, 'aut_label': '56.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '28.a1', '28.c1', '28.d1'], 'contains': ['112.a1', '112.b1'], 'core': '56.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3201, 4279, 6435, 4618], 'generators': [8, 112], 'label': '224.181.56.a1', 'mobius_quo': 2, 'mobius_sub': 56, 'normal_closure': '56.a1', 'normal_contained_in': ['8.a1', '28.a1'], 'normal_contains': ['112.a1', '112.b1'], 'normalizer': '1.a1', 'old_label': '56.a1', 'projective_image': '56.12', 'quotient_action_image': '1.1', 'quotient_action_kernel': '56.12', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '56.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967639
{'ambient': '224.181', 'aut_centralizer_order': 2688, 'aut_label': '56.b1', 'aut_quo_index': 6, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '28.a1', '28.b1', '28.e1', '28.f1'], 'contains': ['112.a1'], 'core': '56.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6990, 6520, 3976, 5480], 'generators': [116], 'label': '224.181.56.b1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.b1', 'normal_contained_in': ['8.c1', '28.a1', '28.b1'], 'normal_contains': ['112.a1'], 'normalizer': '1.a1', 'old_label': '56.b1', 'projective_image': '112.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.3', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967640
{'ambient': '224.181', 'aut_centralizer_order': 1152, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '28.c1', '28.e1'], 'contains': ['112.a1', '112.c1'], 'core': '112.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2014, -1, 7599, -1], 'generators': [2, 8], 'label': '224.181.56.c1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.c1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967641
{'ambient': '224.181', 'aut_centralizer_order': 384, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.d1', '28.d1', '28.e1', '28.f1'], 'contains': ['112.a1'], 'core': '112.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4519, -1, 5907, -1], 'generators': [6], 'label': '224.181.56.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.d1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20967642
{'ambient': '224.181', 'aut_centralizer_order': 576, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '28.c1'], 'contains': ['112.b1', '112.c1'], 'core': '112.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [844, -1, 8764, -1], 'generators': [2, 112], 'label': '224.181.56.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.e1', 'projective_image': '112.33', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967643
{'ambient': '224.181', 'aut_centralizer_order': 32256, 'aut_label': '112.a1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '56.a1', '56.b1', '56.c1', '56.d1'], 'contains': ['224.a1'], 'core': '112.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2887, 4876, 6729, 4577], 'generators': [8], 'label': '224.181.112.a1', 'mobius_quo': -1, 'mobius_sub': -448, 'normal_closure': '112.a1', 'normal_contained_in': ['16.a1', '56.a1', '56.b1'], 'normal_contains': ['224.a1'], 'normalizer': '1.a1', 'old_label': '112.a1', 'projective_image': '112.42', 'quotient_action_image': '1.1', 'quotient_action_kernel': '112.42', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '112.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967644
{'ambient': '224.181', 'aut_centralizer_order': 16128, 'aut_label': '112.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '1.a1', 'complements': ['2.d1'], 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '56.a1', '56.e1'], 'contains': ['224.a1'], 'core': '112.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1421, 3976, 7709, 3797], 'generators': [112], 'label': '224.181.112.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '112.b1', 'normal_contained_in': ['16.b1', '56.a1'], 'normal_contains': ['224.a1'], 'normalizer': '1.a1', 'old_label': '112.b1', 'projective_image': '112.33', 'quotient_action_image': '1.1', 'quotient_action_kernel': '112.33', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '112.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967645
{'ambient': '224.181', 'aut_centralizer_order': 1152, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '56.c1', '56.e1'], 'contains': ['224.a1'], 'core': '224.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [828, -1, 8736, -1], 'generators': [2], 'label': '224.181.112.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '112.c1', 'projective_image': '224.181', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967646
{'ambient': '224.181', 'aut_centralizer_order': 28, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.156667', 'aut_weyl_index': 28, 'centralizer': '8.a1', 'complements': ['112.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.f1', '14.a1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9197, 9167, 1517, 8353], 'generators': [1, 112, 32, 4, 8], 'label': '224.181.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.f1', '14.a1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '56.12', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 20967647
{'ambient': '224.181', 'aut_centralizer_order': None, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '112.a1', '112.b1', '112.c1'], 'contains': [], 'core': '224.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1125, 3976, 7955, 3797], 'generators': [], 'label': '224.181.224.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.a1', 'normal_contained_in': ['32.a1', '112.a1', '112.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '224.a1', 'projective_image': '224.181', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20967648
{'ambient': '224.181', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '2016.dc', 'aut_weyl_index': 16, 'centralizer': '56.a1', 'complements': ['112.b1', '112.c1'], 'conjugacy_class_count': 8, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.e1', '4.f1', '14.d1'], 'core': '2.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [7954, 7466, 3723, 6803], 'generators': [121, 4, 8, 2, 32], 'label': '224.181.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.e1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '112.42', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 20967649
{'ambient': '224.181', 'aut_centralizer_order': 96, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '14.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.b1', '8.e1', '28.c1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1702, 788, 9147, 718], 'generators': [2, 112, 32, 8], 'label': '224.181.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '8.b1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 20967650
{'ambient': '224.181', 'aut_centralizer_order': 224, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '48.45', 'aut_weyl_index': 672, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.c1', '28.a1'], 'core': '4.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6676, 6024, 4887, 5490], 'generators': [4, 32, 8, 112], 'label': '224.181.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.c1', '28.a1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '56.12', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20967651
{'ambient': '224.181', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '28.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.d1', '28.d1'], 'core': '4.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [3876, 2623, 8031, 2391], 'generators': [6, 8, 32, 112], 'label': '224.181.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '56.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 20967652
{'ambient': '224.181', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '28.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.b1', '8.c1', '8.d1', '28.e1'], 'core': '4.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [5441, 4336, 6990, 3951], 'generators': [2, 8, 32, 124], 'label': '224.181.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.b1', '8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '112.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '28.3'}

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.