Finite Group Databasebeta

← Group #13151370

Character table — Group #13151370

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order122222366624663366666661236666666661212224444444412121212666661212122444444661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111-1-1111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-11-11-1-11-1-11111-1-1-1-1-1-1-1-1-111-1
χ51111111111-1-11111111111-1-111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-111-1-1-1-1111111-1-1-111-1
χ61111111111-1-11111111111-1-111111-1-1111-1-111-1-111-1-111-1-1-1-1-111-1-1-1-1-11-1-1-1-111111111-1-1-1-111-1-11-1-11
χ71111111111-1-11111111111-1-111111-1-1111-1-1-1-111-1-111111111-111-1-1-1-1-1-1-11-11-11-1-111111111-1-111-1-1-1-1
χ81111111111-1-11111111111-1-111111-1-1111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-1-111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ91111-1-111111-1-1-1111111111-11-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-111-111111-1-111-1-1-1-11111-1-1
χ101111-1-111111-1-1-1111111111-11-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1-111-111-111-1-111-1-111-1-111-1-111
χ111111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-11111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-11111-1-111-1-11-11-1
χ121111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-1-1-11111-1-111111-1-111-1-1-1-1-111-111-1-111-1-1-1-11111-1-1-11-11
χ131111-1-11111-11-1-111111111-111-1-1-1-1-1-1111111111-1-111111111-1-1-1-1-1111-1-1-11-11-111-1-11111-1-1-1-1-1-1-11-11
χ141111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1111111-1-1-111111-1-1-1-111-1-1-1-11-11-1
χ151111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111-1-111-1-111-1-11111-1-111
χ161111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-111-1-111111111-1-1
χ17222222222222222-122-1-1-1222-122-1-122-1-1-12200220000000000-1-1-1-1-1-1-1-12020020000000-1-1-1-10000-100-1
χ18222222222222222-122-1-1-1222-122-1-122-1-1-12200-2-20000000000-1-1-1-1-1-1-1-1-20-200-20000000111100001001
χ1922222222222222-12-1-1222-122-1-1-122-1-1-1-1-1-1-12200222200-1-1-1-12-1-1-1-12-1-10000200-1-100000000-1-1-1-10000
χ2022222222222222-12-1-1222-122-1-1-122-1-1-1-1-1-1-1-2-200-2-2-2-20011112-1-1-1-12-1-10000-200110000000011110000
χ212222222222-2-2222-122-1-1-12-2-2-122-1-1-2-2-1-1-1-2-2002200000000001-1-111111-20200-20000000-1-1-1-100001001
χ222222222222-2-2222-122-1-1-12-2-2-122-1-1-2-2-1-1-1-2-200-2-200000000001-1-11111120-2002000000011110000-100-1
χ232222222222-2-222-12-1-1222-1-2-2-1-1-12211-1-1-111220022-2-2001111-2-1-111-2110000-200-1-100000000-1-1110000
χ242222222222-2-222-12-1-1222-1-2-2-1-1-12211-1-1-111-2-200-2-22200-1-1-1-1-2-1-111-2110000200110000000011-1-10000
χ252222-2-222222-2-2-22-122-1-1-122-2-1-2-21122-1-1-1-2-200220000000000-111-1-111120-200-20000000-1-1110000-1001
χ262222-2-222222-2-2-22-122-1-1-122-2-1-2-21122-1-1-1-2-200-2-20000000000-111-1-1111-202002000000011-1-10000100-1
χ272222-2-222222-2-2-2-12-1-1222-12-2-111-2-2-1-1-1-1-1112200-2-2-2-2001111211-1-1-2110000200-1-10000000011-1-10000
χ282222-2-222222-2-2-2-12-1-1222-12-2-111-2-2-1-1-1-1-111-2-200222200-1-1-1-1211-1-1-2110000-2001100000000-1-1110000
χ292222-2-22222-22-2-22-122-1-1-12-22-1-2-211-2-2-1-1-1220022000000000011111-1-1-1-20-20020000000-1-1110000100-1
χ302222-2-22222-22-2-22-122-1-1-12-22-1-2-211-2-2-1-1-12200-2-2000000000011111-1-1-120200-2000000011-1-10000-1001
χ312222-2-22222-22-2-2-12-1-1222-1-22-111-2-211-1-1-1-1-12200-2-22200-1-1-1-1-211112-1-10000-200-1-10000000011110000
χ322222-2-22222-22-2-2-12-1-1222-1-22-111-2-211-1-1-1-1-1-2-20022-2-2001111-211112-1-100002001100000000-1-1-1-10000
χ332-22-20022-2-20000222-2-2-22-20020000002-2-200002-2002i−2i2i−2i2i2i−2i−2i00000000000000000002i−2i2-20000000000
χ342-22-20022-2-20000222-2-2-22-20020000002-2-200002-200−2i2i−2i2i−2i−2i2i2i0000000000000000000−2i2i2-20000000000
χ352-22-20022-2-20000222-2-2-22-20020000002-2-20000-22002i−2i−2i2i2i2i−2i−2i0000000000000000000−2i2i-220000000000
χ362-22-20022-2-20000222-2-2-22-20020000002-2-20000-2200−2i2i2i−2i−2i−2i2i2i00000000000000000002i−2i-220000000000
χ372-2-222-22-2-22002-222-2-2-22-220022-22-200-2-22002-2002-20000000002-20000000000002-2000000002-2000000
χ382-2-222-22-2-22002-222-2-2-22-220022-22-200-2-2200-2200-220000000002-2000000000000-2200000000-22000000
χ392-2-222-22-2-22002-2-1211-22-2-100-1-112-2−i3i311-1−i3i32-2002-20000−i3i3−i3i30-11−i3i30−i3i30000000-1100000000-11−i3i30000
χ402-2-222-22-2-22002-2-1211-22-2-100-1-112-2−i3i311-1−i3i3-2200-220000i3−i3i3−i30-11−i3i30−i3i300000001-1000000001-1i3−i30000
χ412-2-222-22-2-22002-2-1211-22-2-100-1-112-2i3−i311-1i3−i32-2002-20000i3−i3i3−i30-11i3−i30i3−i30000000-1100000000-11i3−i30000
χ422-2-222-22-2-22002-2-1211-22-2-100-1-112-2i3−i311-1i3−i3-2200-220000−i3i3−i3i30-11i3−i30i3−i300000001-1000000001-1−i3i30000
χ432-2-22-222-2-2200-2222-2-2-22-22002-22-2200-2-22002-200-22000000000-220000000000002-200000000-22000000
χ442-2-22-222-2-2200-2222-2-2-22-22002-22-2200-2-2200-22002-2000000000-22000000000000-22000000002-2000000
χ452-2-22-222-2-2200-22-1211-22-2-100-11-1-22−i3i311-1i3−i32-200-220000i3−i3i3−i301-1−i3i30i3−i30000000-11000000001-1−i3i30000
χ462-2-22-222-2-2200-22-1211-22-2-100-11-1-22−i3i311-1i3−i3-22002-20000−i3i3−i3i301-1−i3i30i3−i300000001-100000000-11i3−i30000
χ472-2-22-222-2-2200-22-1211-22-2-100-11-1-22i3−i311-1−i3i32-200-220000−i3i3−i3i301-1i3−i30−i3i30000000-11000000001-1i3−i30000
χ482-2-22-222-2-2200-22-1211-22-2-100-11-1-22i3−i311-1−i3i3-22002-20000i3−i3i3−i301-1i3−i30−i3i300000001-100000000-11−i3i30000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2-2-2-2-2111-2-200000000000000-21111-2110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-41-2-2-2-2221112200000000000000211-1-12-1-10000000000000000000000000
χ514444-4-444444-4-4-4-2-2-2-2-2-2-2-24-412222-2-21112200000000000000-2-1-1112-1-10000000000000000000000000
χ524444-4-44444-44-4-4-2-2-2-2-2-2-2-2-441222222111-2-2000000000000002-1-1-1-1-2110000000000000000000000000
χ5344-4-4004-44-4000044-444-4-4-4004000000-44-40000000000000000000000000000000000000000000000000
χ5444-4-4004-44-400004-2-44-222-400-20000002-2200000000000000000000000000000000000000023−2300000000
χ5544-4-4004-44-400004-2-44-222-400-20000002-22000000000000000000000000000000000000000−232300000000
χ5644-4-4004-44-40000-242-24-4-4200-20000002-2200000000000023−23−2323000000000000000000000000000000000
χ5744-4-4004-44-40000-242-24-4-4200-20000002-22000000000000−232323−23000000000000000000000000000000000
χ584-44-40044-4-400004-24-422-2-400-2000000-22200004-40000000000000000000000000000000-220000000000
χ594-44-40044-4-400004-24-422-2-400-2000000-2220000-4400000000000000000000000000000002-20000000000
χ604-44-40044-4-40000-24-22-4-44200-2000000-222000000004i−4i00−2i−2i2i2i000000000000000000000000000000000
χ614-44-40044-4-40000-24-22-4-44200-2000000-22200000000−4i4i002i2i−2i−2i000000000000000000000000000000000
χ624-4-444-44-4-44004-44-2-4-42-22400-24-4-220022-200000000000000000-22000000000000000000000000000000
χ634-4-444-44-4-44004-4-2-2222-22-2001-22-22−2i32i3-1-11−2i32i30000000000000001-1i3−i30i3−i30000000000000000000000000
χ644-4-444-44-4-44004-4-2-2222-22-2001-22-222i3−2i3-1-112i3−2i30000000000000001-1−i3i30−i3i30000000000000000000000000
χ654-4-44-444-4-4400-444-2-4-42-22400-2-442-20022-2000000000000000002-2000000000000000000000000000000
χ664-4-44-444-4-4400-44-2-2222-22-20012-22-2−2i32i3-1-112i3−2i3000000000000000-11i3−i30−i3i30000000000000000000000000
χ674-4-44-444-4-4400-44-2-2222-22-20012-22-22i3−2i3-1-11−2i32i3000000000000000-11−i3i30i3−i30000000000000000000000000
χ68666666-3-3-3-366-3-300000000-3-30000000000000000000022000000000000020200200-1-1-1-1000000000-1-10
χ69666666-3-3-3-366-3-300000000-3-300000000000000000000-2-20000000000000-20-200-2001111000000000110
χ70666666-3-3-3-3-6-6-3-3000000003300000000000000000000220000000000000-20-200200-1-1-1-1000000000110
χ71666666-3-3-3-3-6-6-3-3000000003300000000000000000000-2-2000000000000020200-2001111000000000-1-10
χ726666-6-6-3-3-3-36-63300000000-330000000000000000000022000000000000020-200-20011-1-10000000001-10
χ736666-6-6-3-3-3-36-63300000000-3300000000000000000000-2-20000000000000-20200200-1-111000000000-110
χ746666-6-6-3-3-3-3-6633000000003-300000000000000000000220000000000000-20200-20011-1-1000000000-110
χ756666-6-6-3-3-3-3-6633000000003-300000000000000000000-2-2000000000000020-200200-1-1110000000001-10
χ7688-8-8008-88-80000-4-44-4-4444002000000-22-20000000000000000000000000000000000000000000000000
χ778-88-80088-8-80000-4-4-4444-440020000002-2-20000000000000000000000000000000000000000000000000
χ781212-12-1200-66-6600000000000000000000000000000000000000000000000000000000023−2300000000000000
χ791212-12-1200-66-66000000000000000000000000000000000000000000000000000000000−232300000000000000
χ8012-1212-1200-6-66600000000000000000000000000000000004i−4i00000000000000000000000−2i2i000000000000
χ8112-1212-1200-6-6660000000000000000000000000000000000−4i4i000000000000000000000002i−2i000000000000
χ8212-12-121212-12-666-600-66000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-1212-666-6006-6000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).