Finite Group Databasebeta

← Group #13151340

Character table — Group #13151340

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
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-11-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1111111-1-1-1-111-1-1-1-111
χ61111111111-1-11111111111-1-111111-1-1111-1-111-1-111-1-111-1-1-1-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-111-1-1
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
χ91111-1-111111-1-1-1111111111-11-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-111-111111-1-111-1-1-1-1111-11-1
χ101111-1-111111-1-1-1111111111-11-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1-111-111-111-1-111-1-111-1-111-11-11
χ111111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-11111111111111-1-111-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-11-1-11
χ121111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-1-1-11111-1-111111-1-111-1-1-1-1-111-111-1-1-1-11111-1-111-1-1-111-1
χ131111-1-11111-11-1-111111111-111-1-1-1-1-1-1111111111-1-111111111-1-1-1-1-1111-1-1-11-11-11111-1-1-1-111-1-1-1-1-111-1
χ141111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1111111-1-1-1111-1-11111-1-1-1-1-1-11-1-11
χ151111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111-1-111-1-111-1-11111-11-11
χ161111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-111-1-11111111-11-1
χ17222222222222222-1-1-1222-122-122-1-1-1-1-1-1-1-1-12200222200-1-1-1-12-1-1-1-12-1-10000200-1-100000000-1-1-1-10000
χ18222222222222222-1-1-1222-122-122-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20011112-1-1-1-12-1-10000-200110000000011110000
χ1922222222222222-1222-1-1-1222-1-1-12222-1-1-12200000000220000-1-1-1-1-1-1-1-10202002000000-1-1-1-1000000-1-1
χ2022222222222222-1222-1-1-1222-1-1-12222-1-1-12200000000-2-20000-1-1-1-1-1-1-1-10-20-200-2000000111100000011
χ212222222222-2-2222-1-1-1222-1-2-2-122-1-111-1-1-111220022-2-2001111-2-1-111-2110000-200-1-100000000-1-1110000
χ222222222222-2-2222-1-1-1222-1-2-2-122-1-111-1-1-111-2-200-2-22200-1-1-1-1-2-1-111-2110000200110000000011-1-10000
χ232222222222-2-222-1222-1-1-12-2-2-1-1-122-2-2-1-1-1-2-2000000002200001-1-1111110-20-2002000000-1-1-1-100000011
χ242222222222-2-222-1222-1-1-12-2-2-1-1-122-2-2-1-1-1-2-200000000-2-200001-1-111111020200-20000001111000000-1-1
χ252222-2-222222-2-2-22-1-1-1222-12-2-1-2-211-1-1-1-1-1112200-2-2-2-2001111211-1-1-2110000200-1-10000000011-1-10000
χ262222-2-222222-2-2-22-1-1-1222-12-2-1-2-211-1-1-1-1-111-2-200222200-1-1-1-1211-1-1-2110000-2001100000000-1-1110000
χ272222-2-222222-2-2-2-1222-1-1-122-2-111-2-222-1-1-1-2-200000000220000-111-1-1111020-200-200000011-1-10000001-1
χ282222-2-222222-2-2-2-1222-1-1-122-2-111-2-222-1-1-1-2-200000000-2-20000-111-1-11110-202002000000-1-111000000-11
χ292222-2-22222-22-2-22-1-1-1222-1-22-1-2-21111-1-1-1-1-12200-2-22200-1-1-1-1-211112-1-10000-200-1-10000000011110000
χ302222-2-22222-22-2-22-1-1-1222-1-22-1-2-21111-1-1-1-1-1-2-20022-2-2001111-211112-1-100002001100000000-1-1-1-10000
χ312222-2-22222-22-2-2-1222-1-1-12-22-111-2-2-2-2-1-1-1220000000022000011111-1-1-10-20200-200000011-1-1000000-11
χ322222-2-22222-22-2-2-1222-1-1-12-22-111-2-2-2-2-1-1-12200000000-2-2000011111-1-1-1020-2002000000-1-1110000001-1
χ332-22-2002-2-220000222-22-2-2-20020000002-2-200002-2002i−2i2i−2i2i2i−2i−2i000000000000000002-200002i−2i00000000
χ342-22-2002-2-220000222-22-2-2-20020000002-2-200002-200−2i2i−2i2i−2i−2i2i2i000000000000000002-20000−2i2i00000000
χ352-22-2002-2-220000222-22-2-2-20020000002-2-20000-22002i−2i−2i2i2i2i−2i−2i00000000000000000-220000−2i2i00000000
χ362-22-2002-2-220000222-22-2-2-20020000002-2-20000-2200−2i2i2i−2i−2i−2i2i2i00000000000000000-2200002i−2i00000000
χ372-2-222-22-22-2002-222-2-2-2-2220022-22-200-2-22002-2002-20000000002-20000000000002-2000000002-2000000
χ382-2-222-22-22-2002-222-2-2-2-2220022-22-200-2-2200-2200-220000000002-2000000000000-2200000000-22000000
χ392-2-222-22-22-2002-22-111-2-22-100-12-2-11−i3i311-1−i3i32-2002-20000−i3i3−i3i30-11−i3i30−i3i30000000-1100000000-11−i3i30000
χ402-2-222-22-22-2002-22-111-2-22-100-12-2-11−i3i311-1−i3i3-2200-220000i3−i3i3−i30-11−i3i30−i3i300000001-1000000001-1i3−i30000
χ412-2-222-22-22-2002-22-111-2-22-100-12-2-11i3−i311-1i3−i32-2002-20000i3−i3i3−i30-11i3−i30i3−i30000000-1100000000-11i3−i30000
χ422-2-222-22-22-2002-22-111-2-22-100-12-2-11i3−i311-1i3−i3-2200-220000−i3i3−i3i30-11i3−i30i3−i300000001-1000000001-1−i3i30000
χ432-2-22-222-22-200-2222-2-2-2-222002-22-2200-2-22002-200-22000000000-220000000000002-200000000-22000000
χ442-2-22-222-22-200-2222-2-2-2-222002-22-2200-2-2200-22002-2000000000-22000000000000-22000000002-2000000
χ452-2-22-222-22-200-222-111-2-22-100-1-221-1−i3i311-1i3−i32-200-220000i3−i3i3−i301-1−i3i30i3−i30000000-11000000001-1−i3i30000
χ462-2-22-222-22-200-222-111-2-22-100-1-221-1−i3i311-1i3−i3-22002-20000−i3i3−i3i301-1−i3i30i3−i300000001-100000000-11i3−i30000
χ472-2-22-222-22-200-222-111-2-22-100-1-221-1i3−i311-1−i3i32-200-220000−i3i3−i3i301-1i3−i30−i3i30000000-11000000001-1i3−i30000
χ482-2-22-222-22-200-222-111-2-22-100-1-221-1i3−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
χ5344-4-40044-4-4000044-44-44-4-4004000000-44-40000000000000000000000000000000000000000000000000
χ5444-4-40044-4-400004-22-2-44-4200-20000002-2200000000000023−23−2323000000000000000000000000000000000
χ5544-4-40044-4-400004-22-2-44-4200-20000002-22000000000000−232323−23000000000000000000000000000000000
χ5644-4-40044-4-40000-24-442-22-400-20000002-22000000000000000000000000000000000000023−230000000000
χ5744-4-40044-4-40000-24-442-22-400-20000002-220000000000000000000000000000000000000−23230000000000
χ584-44-4004-4-4400004-2-224-4-4200-2000000-222000000004i−4i00−2i−2i2i2i000000000000000000000000000000000
χ594-44-4004-4-4400004-2-224-4-4200-2000000-22200000000−4i4i002i2i−2i−2i000000000000000000000000000000000
χ604-44-4004-4-440000-244-4-222-400-2000000-22200000000004i−4i000000000000000000000000000−2i2i00000000
χ614-44-4004-4-440000-244-4-222-400-2000000-2220000000000−4i4i0000000000000000000000000002i−2i00000000
χ624-4-444-44-44-4004-4-24-4-422-2400-2-224-40022-200000000000000000-22000000000000000000000000000000
χ634-4-444-44-44-4004-4-2-22222-2-2001-22-22−2i32i3-1-11−2i32i30000000000000001-1i3−i30i3−i30000000000000000000000000
χ644-4-444-44-44-4004-4-2-22222-2-2001-22-222i3−2i3-1-112i3−2i30000000000000001-1−i3i30−i3i30000000000000000000000000
χ654-4-44-444-44-400-44-24-4-422-2400-22-2-440022-2000000000000000002-2000000000000000000000000000000
χ664-4-44-444-44-400-44-2-22222-2-20012-22-2−2i32i3-1-112i3−2i3000000000000000-11i3−i30−i3i30000000000000000000000000
χ674-4-44-444-44-400-44-2-22222-2-20012-22-22i3−2i3-1-11−2i32i3000000000000000-11−i3i30i3−i30000000000000000000000000
χ68666666-3-3-3-366-3-300000000-3-30000000000000022000000000000000000202002000-1-1-1-100000000-1-100
χ69666666-3-3-3-366-3-300000000-3-300000000000000-2-2000000000000000000-20-200-20001111000000001100
χ70666666-3-3-3-3-6-6-3-300000000330000000000000022000000000000000000-20200-2000-1-1-1-1000000001100
χ71666666-3-3-3-3-6-6-3-3000000003300000000000000-2-200000000000000000020-2002000111100000000-1-100
χ726666-6-6-3-3-3-36-63300000000-33000000000000002200000000000000000020-200-2000-1-11100000000-1100
χ736666-6-6-3-3-3-36-63300000000-3300000000000000-2-2000000000000000000-20200200011-1-1000000001-100
χ746666-6-6-3-3-3-3-6633000000003-30000000000000022000000000000000000-20-2002000-1-111000000001-100
χ756666-6-6-3-3-3-3-6633000000003-300000000000000-2-200000000000000000020200-200011-1-100000000-1100
χ7688-8-80088-8-80000-4-44-44-444002000000-22-20000000000000000000000000000000000000000000000000
χ778-88-8008-8-880000-4-4-44-44440020000002-2-20000000000000000000000000000000000000000000000000
χ781212-12-1200-6-6660000000000000000000000000000000000000000000000000000000000023−23000000000000
χ791212-12-1200-6-66600000000000000000000000000000000000000000000000000000000000−2323000000000000
χ8012-1212-1200-666-600000000000000000000000000004-4000000000000000000000000000-2200000000000000
χ8112-1212-1200-666-60000000000000000000000000000-440000000000000000000000000002-200000000000000
χ8212-12-121212-12-66-6600-66000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-1212-66-66006-6000000000000000000000000000000000000000000000000000000000000000000000

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