{"group ", "SmallGroup(180,19)", "also called ", "Sigma60xZ3", "conjclasInfo ", "Conjugacy Classes of group \ Gp\n-----------------------------\n[1] Order 1 Length 1 \n \ Rep Id(Gp)\n\n[2] Order 2 Length 15 \n Rep (1, 2)(3, \ 5)\n\n[3] Order 3 Length 1 \n Rep (6, 7, 8)\n\n[4] \ Order 3 Length 1 \n Rep (6, 8, 7)\n\n[5] Order 3 \ Length 20 \n Rep (2, 4, 5)(6, 8, 7)\n\n[6] Order 3 \ Length 20 \n Rep (2, 5, 4)(6, 7, 8)\n\n[7] Order 3 \ Length 20 \n Rep (1, 4, 3)\n\n[8] Order 5 Length 12 \ \n Rep (1, 4, 5, 3, 2)\n\n[9] Order 5 Length 12 \n \ Rep (1, 5, 2, 4, 3)\n\n[10] Order 6 Length 15 \n Rep (1, \ 4)(2, 5)(6, 7, 8)\n\n[11] Order 6 Length 15 \n Rep (1, \ 4)(2, 5)(6, 8, 7)\n\n[12] Order 15 Length 12 \n Rep (1, 5, \ 2, 4, 3)(6, 8, 7)\n\n[13] Order 15 Length 12 \n Rep (1, 2, \ 3, 5, 4)(6, 7, 8)\n\n[14] Order 15 Length 12 \n Rep (1, 2, \ 3, 5, 4)(6, 8, 7)\n\n[15] Order 15 Length 12 \n Rep (1, 5, \ 2, 4, 3)(6, 7, 8)\n\n\n", "centralizerInfo ", "[\n Permutation group \ acting on a set of cardinality 8\n Order = 180 = 2^2 * 3^2 * 5\n \ (6, 8, 7)\n (1, 2)(4, 5)\n (2, 3)(4, 5)\n (3, 4, 5),\n \ Permutation group acting on a set of cardinality 8\n Order = 12 = 2^2 * \ 3\n (1, 3)(2, 5)\n (1, 2)(3, 5)\n (6, 7, 8),\n \ Permutation group acting on a set of cardinality 8\n Order = 180 = 2^2 * \ 3^2 * 5\n (6, 7, 8)\n (1, 2)(4, 5)\n (2, 3)(4, 5)\n \ (3, 4, 5),\n Permutation group acting on a set of cardinality 8\n \ Order = 180 = 2^2 * 3^2 * 5\n (6, 7, 8)\n (1, 2)(4, 5)\n \ (2, 3)(4, 5)\n (3, 4, 5),\n Permutation group acting on a set of \ cardinality 8\n Order = 9 = 3^2\n (2, 4, 5)\n (6, 8, 7),\n \ Permutation group acting on a set of cardinality 8\n Order = 9 = 3^2\n \ (2, 4, 5)\n (6, 8, 7),\n Permutation group acting on a set of \ cardinality 8\n Order = 9 = 3^2\n (1, 4, 3)\n (6, 8, 7),\n \ Permutation group acting on a set of cardinality 8\n Order = 15 = 3 * 5\n \ (1, 4, 5, 3, 2)\n (6, 7, 8),\n Permutation group acting on a \ set of cardinality 8\n Order = 15 = 3 * 5\n (1, 5, 2, 4, 3)\n \ (6, 7, 8),\n Permutation group acting on a set of cardinality 8\n \ Order = 12 = 2^2 * 3\n (6, 7, 8)\n (1, 2)(4, 5)\n (1, \ 4)(2, 5),\n Permutation group acting on a set of cardinality 8\n Order \ = 12 = 2^2 * 3\n (6, 7, 8)\n (1, 2)(4, 5)\n (1, 4)(2, \ 5),\n Permutation group acting on a set of cardinality 8\n Order = 15 = \ 3 * 5\n (1, 5, 2, 4, 3)\n (6, 7, 8),\n Permutation group \ acting on a set of cardinality 8\n Order = 15 = 3 * 5\n (1, 2, 3, \ 5, 4)\n (6, 7, 8),\n Permutation group acting on a set of \ cardinality 8\n Order = 15 = 3 * 5\n (1, 2, 3, 5, 4)\n (6, \ 7, 8),\n Permutation group acting on a set of cardinality 8\n Order = \ 15 = 3 * 5\n (1, 5, 2, 4, 3)\n (6, 7, 8)\n]\n", "card[group] ", 180, "\[Lambda]max ", 198, "centralgrading[group] ", {15, 12, 15, 15, 9, 9, 9, 15, 15, 12, 12, 15, 15, 15, 15}, "qdimlist ", {1, 1, 1, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1, 1, 1, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 1, 1, 1, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12}, "dimA ", 32400, "horizontalDimensions ", {198, 198, 198, 576, 576, 576, 576, 576, 576, 765, 765, 765, 954, 954, 954, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 198, 198, 198, 576, 576, 576, 576, 576, 576, 765, 765, 765, 954, 954, 954, 198, 198, 198, 576, 576, 576, 576, 576, 576, 765, 765, 765, 954, 954, 954, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 3213, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 2448, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989, 1989}, "dimB ", 870302070, "smallrank ", 15, "smalldim ", {1, 1, 1, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5}}