{
  "cyclic_prime_square": {
    "2": [
      2
    ],
    "3": [
      3
    ],
    "5": [
      5
    ]
  },
  "heisenberg_3_rank1": {
    "all_subgroup_count": 19,
    "allowed_subgroup_classes": [
      {
        "automorphism_order": 27,
        "conjugacy_class_size": 1,
        "multiplicity_weight": 9,
        "normalizer_order": 27,
        "subgroup_order": 1
      },
      {
        "automorphism_order": 3,
        "conjugacy_class_size": 3,
        "multiplicity_weight": 3,
        "normalizer_order": 9,
        "subgroup_order": 3
      },
      {
        "automorphism_order": 3,
        "conjugacy_class_size": 3,
        "multiplicity_weight": 3,
        "normalizer_order": 9,
        "subgroup_order": 3
      },
      {
        "automorphism_order": 3,
        "conjugacy_class_size": 3,
        "multiplicity_weight": 3,
        "normalizer_order": 9,
        "subgroup_order": 3
      },
      {
        "automorphism_order": 3,
        "conjugacy_class_size": 3,
        "multiplicity_weight": 3,
        "normalizer_order": 9,
        "subgroup_order": 3
      }
    ],
    "center_order": 3,
    "group_order": 27,
    "isotropic_counts": {
      "0": 1,
      "1": 4
    },
    "series": {
      "0": {
        "isomorphism_classes": 1,
        "mass": "1"
      },
      "12": {
        "isomorphism_classes": 39,
        "mass": "44/243"
      },
      "15": {
        "isomorphism_classes": 66,
        "mass": "248/3645"
      },
      "18": {
        "isomorphism_classes": 105,
        "mass": "1517/65610"
      },
      "21": {
        "isomorphism_classes": 159,
        "mass": "5014/688905"
      },
      "24": {
        "isomorphism_classes": 231,
        "mass": "892/413343"
      },
      "27": {
        "isomorphism_classes": 325,
        "mass": "67537/111602610"
      },
      "3": {
        "isomorphism_classes": 4,
        "mass": "4/3"
      },
      "6": {
        "isomorphism_classes": 10,
        "mass": "8/9"
      },
      "9": {
        "isomorphism_classes": 21,
        "mass": "35/81"
      }
    }
  },
  "heisenberg_formula_counts": {
    "p=3,r=2": [
      1,
      40,
      40
    ],
    "p=3,r=3": [
      1,
      364,
      3640,
      1120
    ],
    "p=5,r=2": [
      1,
      156,
      156
    ]
  },
  "method": "Exact subgroup enumeration from multiplication tables",
  "sl2_f5": {
    "all_subgroup_count": 76,
    "allowed_subgroup_classes": [
      {
        "automorphism_order": 120,
        "conjugacy_class_size": 1,
        "multiplicity_weight": 60,
        "normalizer_order": 120,
        "subgroup_order": 1
      },
      {
        "automorphism_order": 4,
        "conjugacy_class_size": 10,
        "multiplicity_weight": 20,
        "normalizer_order": 12,
        "subgroup_order": 3
      },
      {
        "automorphism_order": 4,
        "conjugacy_class_size": 6,
        "multiplicity_weight": 12,
        "normalizer_order": 20,
        "subgroup_order": 5
      }
    ],
    "center_order": 2,
    "group_order": 120,
    "multiplicities": {
      "computed_through": 100,
      "positive_members": [
        12,
        20,
        24,
        32,
        36,
        40,
        44,
        48,
        52,
        56,
        60,
        64,
        68,
        72,
        76,
        80,
        84,
        88,
        92,
        96,
        100
      ],
      "weights": [
        12,
        20,
        60
      ]
    },
    "series": {
      "0": {
        "isomorphism_classes": 1,
        "mass": "1"
      },
      "100": {
        "isomorphism_classes": 3,
        "mass": "1057/3932160"
      },
      "12": {
        "isomorphism_classes": 1,
        "mass": "1/4"
      },
      "20": {
        "isomorphism_classes": 1,
        "mass": "1/4"
      },
      "24": {
        "isomorphism_classes": 1,
        "mass": "1/32"
      },
      "32": {
        "isomorphism_classes": 1,
        "mass": "1/16"
      },
      "36": {
        "isomorphism_classes": 1,
        "mass": "1/384"
      },
      "40": {
        "isomorphism_classes": 1,
        "mass": "1/32"
      },
      "44": {
        "isomorphism_classes": 1,
        "mass": "1/128"
      },
      "48": {
        "isomorphism_classes": 1,
        "mass": "1/6144"
      },
      "52": {
        "isomorphism_classes": 1,
        "mass": "1/128"
      },
      "56": {
        "isomorphism_classes": 1,
        "mass": "1/1536"
      },
      "60": {
        "isomorphism_classes": 3,
        "mass": "269/24576"
      },
      "64": {
        "isomorphism_classes": 1,
        "mass": "1/1024"
      },
      "68": {
        "isomorphism_classes": 1,
        "mass": "1/24576"
      },
      "72": {
        "isomorphism_classes": 3,
        "mass": "1613/589824"
      },
      "76": {
        "isomorphism_classes": 1,
        "mass": "1/12288"
      },
      "80": {
        "isomorphism_classes": 3,
        "mass": "221/98304"
      },
      "84": {
        "isomorphism_classes": 3,
        "mass": "5645/16515072"
      },
      "88": {
        "isomorphism_classes": 1,
        "mass": "1/196608"
      },
      "92": {
        "isomorphism_classes": 3,
        "mass": "1325/2359296"
      },
      "96": {
        "isomorphism_classes": 3,
        "mass": "15053/528482304"
      }
    }
  }
}