{"group ", "SmallGroup(1080,260)", "also called ", "Sigma1080", "conjclasInfo ", "Conjugacy Classes of group \ Gp\n-----------------------------\n[1] Order 1 Length 1 \n \ Rep Id(Gp)\n\n[2] Order 2 Length 45 \n Rep (1, 6)(2, \ 9)(3, 17)(4, 12)(5, 18)(8, 13)\n\n[3] Order 3 Length 1 \n \ Rep (1, 4, 2)(3, 8, 5)(6, 12, 9)(7, 15, 10)(11, 14, 16)(13, 18, 17)\n\n[4] \ Order 3 Length 1 \n Rep (1, 2, 4)(3, 5, 8)(6, 9, 12)(7, \ 10, 15)(11, 16, 14)(13, 17, 18)\n\n[5] Order 3 Length 120 \n \ Rep (1, 3, 6)(2, 5, 9)(4, 8, 12)(7, 14, 13)(10, 11, 17)(15, 16, 18)\n\n[6] \ Order 3 Length 120 \n Rep (1, 7, 13)(2, 10, 17)(3, 5, \ 8)(4, 15, 18)(6, 12, 9)\n\n[7] Order 4 Length 90 \n Rep \ (1, 13, 6, 8)(2, 17, 9, 3)(4, 18, 12, 5)(7, 14)(10, 11)(15, 16)\n\n[8] \ Order 5 Length 72 \n Rep (1, 14, 13, 3, 9)(2, 11, 17, 5, \ 12)(4, 16, 18, 8, 6)\n\n[9] Order 5 Length 72 \n Rep (1, \ 13, 9, 14, 3)(2, 17, 12, 11, 5)(4, 18, 6, 16, 8)\n\n[10] Order 6 \ Length 45 \n Rep (1, 4, 2)(3, 18, 5, 13, 8, 17)(6, 11, 9, 16, 12, \ 14)(7, 15, 10)\n\n[11] Order 6 Length 45 \n Rep (1, 2, \ 4)(3, 17, 8, 13, 5, 18)(6, 14, 12, 16, 9, 11)(7, 10, 15)\n\n[12] Order 12 \ Length 90 \n Rep (1, 7, 4, 15, 2, 10)(3, 6, 18, 11, 5, 9, 13, \ 16, 8, 12, 17, 14)\n\n[13] Order 12 Length 90 \n Rep (1, \ 10, 2, 15, 4, 7)(3, 9, 17, 11, 8, 6, 13, 14, 5, 12, 18, 16)\n\n[14] Order \ 15 Length 72 \n Rep (1, 14, 3, 10, 17, 4, 16, 8, 7, 13, 2, \ 11, 5, 15, 18)(6, 9, 12)\n\n[15] Order 15 Length 72 \n Rep \ (1, 3, 17, 16, 7, 2, 5, 18, 14, 10, 4, 8, 13, 11, 15)(6, 12, 9)\n\n[16] \ Order 15 Length 72 \n Rep (1, 8, 18, 16, 15, 4, 5, 17, 11, \ 10, 2, 3, 13, 14, 7)(6, 9, 12)\n\n[17] Order 15 Length 72 \n \ Rep (1, 11, 8, 10, 18, 2, 16, 3, 15, 13, 4, 14, 5, 7, 17)(6, 12, 9)\n\n\n", "centralizerInfo ", "[\n Permutation group acting on a set of cardinality \ 18\n Order = 1080 = 2^3 * 3^3 * 5\n (1, 3)(2, 5)(4, 8)(11, 17)(13, \ 14)(16, 18)\n (3, 6)(5, 9)(7, 13)(8, 12)(10, 17)(15, 18)\n (6, \ 13)(7, 16)(9, 17)(10, 14)(11, 15)(12, 18)\n (6, 10)(7, 12)(9, 15)(11, \ 17)(13, 14)(16, 18),\n Permutation group acting on a set of cardinality \ 18\n Order = 24 = 2^3 * 3\n (1, 18, 2, 13, 4, 17)(3, 6, 5, 9, 8, \ 12)(7, 15, 10)(11, 14, 16)\n (3, 17)(5, 18)(7, 14)(8, 13)(10, 11)(15, \ 16),\n Permutation group acting on a set of cardinality 18\n Order = \ 1080 = 2^3 * 3^3 * 5\n (1, 3)(2, 5)(4, 8)(11, 17)(13, 14)(16, 18)\n \ (3, 6)(5, 9)(7, 13)(8, 12)(10, 17)(15, 18)\n (6, 13)(7, 16)(9, \ 17)(10, 14)(11, 15)(12, 18)\n (6, 10)(7, 12)(9, 15)(11, 17)(13, \ 14)(16, 18),\n Permutation group acting on a set of cardinality 18\n \ Order = 1080 = 2^3 * 3^3 * 5\n (1, 3)(2, 5)(4, 8)(11, 17)(13, 14)(16, \ 18)\n (3, 6)(5, 9)(7, 13)(8, 12)(10, 17)(15, 18)\n (6, 13)(7, \ 16)(9, 17)(10, 14)(11, 15)(12, 18)\n (6, 10)(7, 12)(9, 15)(11, 17)(13, \ 14)(16, 18),\n Permutation group acting on a set of cardinality 18\n \ Order = 9 = 3^2\n (1, 8, 9)(2, 3, 12)(4, 5, 6)(7, 16, 17)(10, 14, \ 18)(11, 13, 15)\n (1, 3, 6)(2, 5, 9)(4, 8, 12)(7, 14, 13)(10, 11, \ 17)(15, 16, 18),\n Permutation group acting on a set of cardinality 18\n \ Order = 9 = 3^2\n (1, 18, 10)(2, 13, 15)(3, 5, 8)(4, 17, 7)(11, 14, \ 16)\n (1, 7, 13)(2, 10, 17)(3, 5, 8)(4, 15, 18)(6, 12, 9),\n \ Permutation group acting on a set of cardinality 18\n Order = 12 = 2^2 * \ 3\n (1, 17, 12, 8, 2, 18, 6, 3, 4, 13, 9, 5)(7, 11, 15, 14, 10, 16),\n \ Permutation group acting on a set of cardinality 18\n Order = 15 = 3 * \ 5\n (1, 12, 8, 13, 11, 4, 9, 5, 18, 14, 2, 6, 3, 17, 16)(7, 10, 15)\n \ (1, 14, 13, 3, 9)(2, 11, 17, 5, 12)(4, 16, 18, 8, 6),\n Permutation \ group acting on a set of cardinality 18\n Order = 15 = 3 * 5\n (1, \ 12, 8, 13, 11, 4, 9, 5, 18, 14, 2, 6, 3, 17, 16)(7, 10, 15)\n (1, 13, \ 9, 14, 3)(2, 17, 12, 11, 5)(4, 18, 6, 16, 8),\n Permutation group acting \ on a set of cardinality 18\n Order = 24 = 2^3 * 3\n (1, 4, 2)(3, \ 14, 5, 11, 8, 16)(6, 13, 9, 17, 12, 18)(7, 15, 10)\n (1, 15)(2, 7)(4, \ 10)(6, 16)(9, 14)(11, 12),\n Permutation group acting on a set of \ cardinality 18\n Order = 24 = 2^3 * 3\n (1, 2, 4)(3, 6, 8, 12, 5, \ 9)(7, 10, 15)(11, 17, 14, 13, 16, 18)\n (1, 15)(2, 7)(4, 10)(6, 16)(9, \ 14)(11, 12),\n Permutation group acting on a set of cardinality 18\n \ Order = 12 = 2^2 * 3\n (1, 7, 4, 15, 2, 10)(3, 6, 18, 11, 5, 9, 13, \ 16, 8, 12, 17, 14),\n Permutation group acting on a set of cardinality \ 18\n Order = 12 = 2^2 * 3\n (1, 10, 2, 15, 4, 7)(3, 9, 17, 11, 8, \ 6, 13, 14, 5, 12, 18, 16),\n Permutation group acting on a set of \ cardinality 18\n Order = 15 = 3 * 5\n (1, 14, 3, 10, 17, 4, 16, 8, \ 7, 13, 2, 11, 5, 15, 18)(6, 9, 12)\n (1, 13, 10, 5, 16)(2, 17, 15, 8, \ 14)(3, 11, 4, 18, 7),\n Permutation group acting on a set of cardinality \ 18\n Order = 15 = 3 * 5\n (1, 17, 7, 5, 14, 4, 13, 15, 3, 16, 2, \ 18, 10, 8, 11)(6, 9, 12)\n (1, 13, 10, 5, 16)(2, 17, 15, 8, 14)(3, 11, \ 4, 18, 7),\n Permutation group acting on a set of cardinality 18\n \ Order = 15 = 3 * 5\n (1, 8, 18, 16, 15, 4, 5, 17, 11, 10, 2, 3, 13, \ 14, 7)(6, 9, 12)\n (1, 13, 10, 5, 16)(2, 17, 15, 8, 14)(3, 11, 4, 18, \ 7),\n Permutation group acting on a set of cardinality 18\n Order = 15 \ = 3 * 5\n (1, 14, 3, 10, 17, 4, 16, 8, 7, 13, 2, 11, 5, 15, 18)(6, 9, \ 12)\n (1, 13, 10, 5, 16)(2, 17, 15, 8, 14)(3, 11, 4, 18, 7)\n]\n", "card[group] ", 1080, "\[Lambda]max ", 240, "centralgrading[group] ", {17, 15, 17, 17, 9, 9, 12, 15, 15, 15, 15, 12, 12, 15, 15, 15, 15}, "qdimlist ", {1, 3, 3, 3, 3, 5, 5, 6, 6, 8, 8, 9, 9, 9, 10, 15, 15, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 90, 90, 90, 1, 3, 3, 3, 3, 5, 5, 6, 6, 8, 8, 9, 9, 9, 10, 15, 15, 1, 3, 3, 3, 3, 5, 5, 6, 6, 8, 8, 9, 9, 9, 10, 15, 15, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 90, 90, 90, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72}, "dimA ", 1166400, "horizontalDimensions ", {240, 669, 669, 669, 669, 1119, 1119, 1350, 1350, 1791, 1791, 2022, 2010, 2010, 2226, 3336, 3336, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 16752, 16752, 16752, 240, 669, 669, 669, 669, 1119, 1119, 1350, 1350, 1791, 1791, 2022, 2010, 2010, 2226, 3336, 3336, 240, 669, 669, 669, 669, 1119, 1119, 1350, 1350, 1791, 1791, 2022, 2010, 2010, 2226, 3336, 3336, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 21822, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 16752, 16752, 16752, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 8382, 16752, 16752, 16752, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 16512, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353, 13353}, "dimB ", 39650423346, "smallrank ", 17, "smalldim ", {1, 3, 3, 3, 3, 5, 5, 6, 6, 8, 8, 9, 9, 9, 10, 15, 15}}