data:
- - character_diagonal:
    - 1
    - 1
    - 4
    - 3
    - 6
    - 26
    - 27
    - 40
    - 57
    - 26
    - 16
    - 125
    - 142
    - 315
    - 602
    - 281
    - 298
    - 660
    - 541
    - 147
    character_matrix:
    - - 1
      - 0
      - 0
      - 0
      - 0
      - 0
      - 1
      - 2
      - 0
      - 0
      - 0
      - 1
      - 0
      - 0
      - 2
    - - 0
      - 1
      - 0
      - 1
      - 0
      - 4
      - 0
      - 0
      - 5
      - 0
      - 3
      - 0
      - 7
      - 11
      - 0
    - - 0
      - 0
      - 4
      - 0
      - 2
      - 0
      - 6
      - 10
      - 0
      - 4
      - 0
      - 14
      - 0
      - 0
      - 30
    - - 0
      - 1
      - 0
      - 3
      - 0
      - 6
      - 0
      - 0
      - 9
      - 0
      - 5
      - 0
      - 15
      - 21
      - 0
    - - 0
      - 0
      - 2
      - 0
      - 6
      - 0
      - 10
      - 8
      - 0
      - 10
      - 0
      - 22
      - 0
      - 0
      - 40
    - - 0
      - 4
      - 0
      - 6
      - 0
      - 26
      - 0
      - 0
      - 36
      - 0
      - 18
      - 0
      - 56
      - 82
      - 0
    - - 1
      - 0
      - 6
      - 0
      - 10
      - 0
      - 27
      - 26
      - 0
      - 22
      - 0
      - 55
      - 0
      - 0
      - 114
    - - 2
      - 0
      - 10
      - 0
      - 8
      - 0
      - 26
      - 40
      - 0
      - 22
      - 0
      - 60
      - 0
      - 0
      - 136
    - - 0
      - 5
      - 0
      - 9
      - 0
      - 36
      - 0
      - 0
      - 57
      - 0
      - 27
      - 0
      - 87
      - 131
      - 0
    - - 0
      - 0
      - 4
      - 0
      - 10
      - 0
      - 22
      - 22
      - 0
      - 26
      - 0
      - 50
      - 0
      - 0
      - 108
    - - 0
      - 3
      - 0
      - 5
      - 0
      - 18
      - 0
      - 0
      - 27
      - 0
      - 16
      - 0
      - 42
      - 65
      - 0
    - - 1
      - 0
      - 14
      - 0
      - 22
      - 0
      - 55
      - 60
      - 0
      - 50
      - 0
      - 125
      - 0
      - 0
      - 264
    - - 0
      - 7
      - 0
      - 15
      - 0
      - 56
      - 0
      - 0
      - 87
      - 0
      - 42
      - 0
      - 142
      - 207
      - 0
    - - 0
      - 11
      - 0
      - 21
      - 0
      - 82
      - 0
      - 0
      - 131
      - 0
      - 65
      - 0
      - 207
      - 315
      - 0
    - - 2
      - 0
      - 30
      - 0
      - 40
      - 0
      - 114
      - 136
      - 0
      - 108
      - 0
      - 264
      - 0
      - 0
      - 602
    component_group: '6.2'
    component_group_number: 2
    components: 6
    counts:
    - - a_1
      - - - 0
          - 5
    - - a_2
      - - - 0
          - 4
        - - 3
          - 1
    - - a_3
      - - - 0
          - 3
    - - (a_1,a_2)
      - - - (0,0)
          - 4
        - - (0,3)
          - 1
    - - (a_1,a_3)
      - - - (0,0)
          - 3
    - - (a_2,a_3)
      - - - (0,0)
          - 2
        - - (3,0)
          - 1
    - - (a_1,a_2,a_3)
      - - - (0,0,0)
          - 2
        - - (0,3,0)
          - 1
    degree: 6
    first_a2_moment: 1
    fourth_trace_moment: 15
    gens: \begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 \\-1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 &
      0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 &
      0 & -1 & 0 \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0
      & 0 & 0 & 1\\1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 &
      0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\\end{bmatrix}
    id: 86
    identity_component: U(1)^3
    label: 1.6.H.6.2a
    label_components:
    - 1
    - 6
    - 7
    - 6
    - 2
    - 0
    maximal: true
    moments:
    - - a_1
      - 1
      - 0
      - 1
      - 0
      - 15
      - 0
      - 310
      - 0
      - 7455
      - 0
      - 195426
      - 0
      - 5416026
    - - a_2
      - 1
      - 1
      - 5
      - 35
      - 321
      - 3411
      - 39143
      - 469785
      - 5810745
      - 73496123
      - 946025115
      - 12351138405
      - 163163777307
    - - a_3
      - 1
      - 0
      - 6
      - 0
      - 822
      - 0
      - 184860
      - 0
      - 48884710
      - 0
      - 14140557396
      - 0
      - 4333208882772
    name: H_{abc,s}
    pretty: H_{abc,s}
    rational: true
    real_dimension: 3
    second_trace_moment: 1
    simplex:
    - 1
    - 1
    - 5
    - 2
    - 7
    - 15
    - 6
    - 35
    - 18
    - 65
    - 38
    - 141
    - 310
    - 48
    - 321
    - 178
    - 104
    - 675
    - 390
    - 1495
    - 860
    - 3330
    - 7455
    - 500
    - 3411
    - 288
    - 1926
    - 1104
    - 7533
    - 4294
    - 2456
    - 16917
    - 9620
    - 38130
    - 21630
    - 86205
    - 195426
    - 822
    - 5580
    - 39143
    - 3180
    - 22074
    - 12516
    - 88243
    - 7112
    - 49818
    - 28184
    - 200151
    - 112780
    - 63680
    - 455110
    - 255990
    - 1037099
    - 582372
    - 2367918
    - 5416026
    st0_label: 1.6.H
    subgroup_multiplicities:
    - 1
    - 1
    subgroups:
    - 1.6.H.3.1a
    - 1.6.H.2.1a
    supgroup_multiplicities: []
    supgroups: []
    trace_histogram: data:image/png;base64,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
    trace_zero_density: 5/6
    weight: 1
    zvector:
    - 5
    - 0
    - 4
    - 0
    - 0
    - 1
    - 3
    - 0
    - 4
    - 0
    - 0
    - 1
    - 3
    - 0
    - 2
    - 0
    - 0
    - 1
    - 0
    - 2
    - 0
    - 0
    - 1
- - degree: 6
    description: '\left\{\begin{bmatrix}A&0&0\\0&B&0\\0&0&C\end{bmatrix}: A,B,C\in\mathrm{U}(1)\subseteq\mathrm{SU}(2)\right\}'
    hodge_circle: u\mapsto\mathrm{diag}(u,\bar u, u, \bar u, u, \bar u)
    id: 18
    label: 1.6.H
    label_components:
    - 1
    - 6
    - 7
    name: U(1)^3
    pretty: \mathrm{U}(1)^3
    real_dimension: 3
    symplectic_form: \begin{bmatrix}J_2&0&0\\0&J_2&0\\0&0&J_2\end{bmatrix},\ J_2:=\begin{bmatrix}0&1\\-1&0\end{bmatrix}
    weight: 1
- - Agroup: true
    Zgroup: true
    abelian: true
    abelian_quotient: '6.2'
    all_subgroups_known: true
    almost_simple: false
    aut_gens:
    - - 1
    - - 5
    aut_group: '2.1'
    aut_order: 2
    aut_stats:
    - - 1
      - 1
      - 1
      - 1
    - - 2
      - 1
      - 1
      - 1
    - - 3
      - 1
      - 2
      - 1
    - - 6
      - 1
      - 2
      - 1
    cc_stats:
    - - 1
      - 1
      - 1
    - - 2
      - 1
      - 1
    - - 3
      - 1
      - 2
    - - 6
      - 1
      - 2
    center_label: '6.2'
    central_product: true
    central_quotient: '1.1'
    commutator_count: 0
    commutator_label: '1.1'
    complements_known: true
    complete: false
    complex_characters_known: true
    composition_factors:
    - '2.1'
    - '3.1'
    composition_length: 2
    counter: 2
    cyclic: true
    derived_length: 1
    direct_factorization:
    - - '2.1'
      - 1
    - - '3.1'
      - 1
    direct_product: true
    div_stats:
    - - 1
      - 1
      - 1
      - 1
    - - 2
      - 1
      - 1
      - 1
    - - 3
      - 1
      - 2
      - 1
    - - 6
      - 1
      - 2
      - 1
    element_repr_type: PC
    elementary: 6
    eulerian_function: 1
    exponent: 6
    exponents_of_order:
    - 1
    - 1
    factors_of_aut_order:
    - 2
    factors_of_order:
    - 2
    - 3
    faithful_reps:
    - - 1
      - 0
      - 2
    frattini_label: '1.1'
    frattini_quotient: '6.2'
    hash: 2
    hyperelementary: 6
    id: 7
    irrC_degree: 1
    irrQ_degree: 2
    irrep_stats:
    - - 1
      - 6
    label: '6.2'
    linC_degree: 1
    linFp_degree: null
    linFq_degree: null
    linQ_degree: 2
    maximal_subgroups_known: true
    metabelian: true
    metacyclic: true
    monomial: true
    name: C6
    ngens: 2
    nilpotency_class: 1
    nilpotent: true
    normal_counts: null
    normal_index_bound: null
    normal_order_bound: null
    normal_subgroups_known: true
    number_autjugacy_classes: 4
    number_characteristic_subgroups: 4
    number_conjugacy_classes: 6
    number_divisions: 4
    number_normal_subgroups: 4
    number_subgroup_autclasses: 4
    number_subgroup_classes: 4
    number_subgroups: 4
    old_label: null
    order: 6
    order_factorization_type: 11
    order_stats:
    - - 1
      - 1
    - - 2
      - 1
    - - 3
      - 2
    - - 6
      - 2
    outer_equivalence: false
    outer_group: '2.1'
    outer_order: 2
    pc_rank: 1
    perfect: false
    permutation_degree: 5
    pgroup: 0
    primary_abelian_invariants:
    - 2
    - 3
    quasisimple: false
    rank: 1
    rational: false
    rational_characters_known: true
    ratrep_stats:
    - - 1
      - 2
    - - 2
      - 2
    representations:
      GLFp:
        d: 2
        gens:
        - 31
        - 56
        p: 3
      GLZ:
        b: 3
        d: 2
        gens:
        - 73
      PC:
        code: 21
        gens:
        - 1
        pres:
        - 2
        - -2
        - -3
        - 4
      Perm:
        d: 5
        gens:
        - 24
        - 4
    schur_multiplier: []
    semidirect_product: true
    simple: false
    smith_abelian_invariants:
    - 6
    solvability_type: 0
    solvable: true
    subgroup_inclusions_known: true
    subgroup_index_bound: 0
    supersolvable: true
    sylow_subgroups_known: true
    tex_name: C_6
    transitive_degree: 6
    wreath_data: null
    wreath_product: false
label_cols:
- label
- name
- label
labels:
- 1.6.H.6.2a
- U(1)^3
- '6.2'
tables:
- gps_st
- gps_st0
- gps_groups
timestamp: '2024-04-23T19:22:34.122843'