Finite Group Databasebeta

← Group #13151336

Character table — Group #13151336

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order1222223666246633666666612222236666666661212224444444466666666612121224444466661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-1111111111-1-1111-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1
χ61111111111-1-11111111111-1-1111111111-1-1111-1-111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-1-1-111111111-1-1
χ91111-1-111111-1-1-1111111111-111111-1-1-1-111111-1-1-1-111-1-111-1-111111-1-111-1-1-111-11-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111-1-111111-1-1-1111111111-111111-1-1-1-111111-1-1-1-1-1-111-1-11111111-1-111-1-1-11-11-11-1-1-111-1-111-1-1-1-111-11-11
χ111111-1-111111-1-1-1111111111-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-111-1-1-1-11-1-111-1-1-1-11-1-11111-1-111-1-111-1-1111-1-11
χ121111-1-111111-1-1-1111111111-1-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-11-1-111-1-1-1-1-111-1111-1-1-1-1111111-1-1-111-1
χ131111-1-11111-11-1-111111111-1111111-1-1-1-1-1-111111-1-111-1-111-1-11111-1-1-1-1-1111-1-11-111-1-1-1-111-1-11111-1-1-11-11
χ141111-1-11111-11-1-111111111-1111111-1-1-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1111-11-11-11-1-1-1-1-1-11111-1-1111-11-1
χ151111-1-11111-11-1-111111111-11-1-1-1-11-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-111-1-1111111-1-1-1-1-1-111-111-1
χ161111-1-11111-11-1-111111111-11-1-1-1-11-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-11-11111-1-111-1-111-1-11-1-11
χ17222222222222222-1-1-122-12222222-122-1-1-1-1-1-1-1-1-12200000000-1-1-1-12-1-1-1-12-1-1200002-1-1-1-10000-1-100000000
χ18222222222222222-1-1-122-1222-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-20000000011112-1-1-1-12-1-1-20000-2111100001100000000
χ1922222222222222-1222-1-12-1220000-1-1-12222-1-1-12200000022220000-1-1-1-1-1-1-1-10002200000000000-1-1-1-100-1-1
χ2022222222222222-1222-1-12-1220000-1-1-12222-1-1-122000000-2-2-2-20000-1-1-1-1-1-1-1-1000-2-20000000000011110011
χ212222222222-2-2222-1-1-122-12-2-22222-122-1-111-1-1-1112200000000-1-1-1-1-2-1-111-211-20000-2-1-11100001100000000
χ222222222222-2-2222-1-1-122-12-2-2-2-2-2-2-122-1-111-1-1-111-2-2000000001111-2-1-111-21120000211-1-10000-1-100000000
χ232222222222-2-222-1222-1-12-1-2-20000-1-1-122-2-2-1-1-1-2-2000000222200001-1-111111000-2-200000000000-1-1-1-10011
χ242222222222-2-222-1222-1-12-1-2-20000-1-1-122-2-2-1-1-1-2-2000000-2-2-2-200001-1-1111110002200000000000111100-1-1
χ252222-2-222222-2-2-22-1-1-122-122-22222-1-2-211-1-1-1-1-111-2-200000000-1-1-1-1211-1-1-21120000-211-1-100001100000000
χ262222-2-222222-2-2-22-1-1-122-122-2-2-2-2-2-1-2-211-1-1-1-1-11122000000001111211-1-1-211-200002-1-1110000-1-100000000
χ272222-2-222222-2-2-2-1222-1-12-12-20000-111-2-222-1-1-1-2-200000022-2-20000-111-1-11110002-200000000000-1-11100-11
χ282222-2-222222-2-2-2-1222-1-12-12-20000-111-2-222-1-1-1-2-2000000-2-2220000-111-1-1111000-220000000000011-1-1001-1
χ292222-2-22222-22-2-22-1-1-122-12-222222-1-2-21111-1-1-1-1-1-2-200000000-1-1-1-1-211112-1-1-20000211110000-1-100000000
χ302222-2-22222-22-2-22-1-1-122-12-22-2-2-2-2-1-2-21111-1-1-1-1-122000000001111-211112-1-120000-2-1-1-1-100001100000000
χ312222-2-22222-22-2-2-1222-1-12-1-220000-111-2-2-2-2-1-1-12200000022-2-2000011111-1-1-1000-2200000000000-1-111001-1
χ322222-2-22222-22-2-2-1222-1-12-1-220000-111-2-2-2-2-1-1-122000000-2-222000011111-1-1-10002-20000000000011-1-100-11
χ3322-2-20022-2-20000222-22-2-2-20022-2-220000002-2-20000002i−2i002i−2i22-2-2000000000000000000002i−2i00002i−2i0000
χ3422-2-20022-2-20000222-22-2-2-20022-2-220000002-2-2000000−2i2i00−2i2i22-2-200000000000000000000−2i2i0000−2i2i0000
χ3522-2-20022-2-20000222-22-2-2-200-2-22220000002-2-20000002i−2i00−2i2i-2-222000000000000000000002i−2i0000−2i2i0000
χ3622-2-20022-2-20000222-22-2-2-200-2-22220000002-2-2000000−2i2i002i−2i-2-22200000000000000000000−2i2i00002i−2i0000
χ372-22-2002-22-2000022-22-22-2-2002-22-22000000-22-200002i−2i002i−2i002-22-20000000000000000002i−2i00002i−2i000000
χ382-22-2002-22-2000022-22-22-2-2002-22-22000000-22-20000−2i2i00−2i2i002-22-2000000000000000000−2i2i0000−2i2i000000
χ392-22-2002-22-2000022-22-22-2-200-22-222000000-22-200002i−2i00−2i2i00-22-220000000000000000002i−2i0000−2i2i000000
χ402-22-2002-22-2000022-22-22-2-200-22-222000000-22-20000−2i2i002i−2i00-22-22000000000000000000−2i2i00002i−2i000000
χ412-2-222-22-2-22002-222-2-2-2-222002-2-2222-22-200-2-22002-2000000002-2-2202-2000000000002-20000000000000000
χ422-2-222-22-2-22002-222-2-2-2-22200-222-222-22-200-2-2200-2200000000-222-202-200000000000-220000000000000000
χ432-2-222-22-2-22002-22-111-2-2-12002-2-22-12-2-11−i3i311-1−i3i32-200000000-111-10-11−i3i30−i3i3000000-11−i3i30000−i3i300000000
χ442-2-222-22-2-22002-22-111-2-2-12002-2-22-12-2-11i3−i311-1i3−i32-200000000-111-10-11i3−i30i3−i3000000-11i3−i30000i3−i300000000
χ452-2-222-22-2-22002-22-111-2-2-1200-222-2-12-2-11−i3i311-1−i3i3-22000000001-1-110-11−i3i30−i3i30000001-1i3−i30000i3−i300000000
χ462-2-222-22-2-22002-22-111-2-2-1200-222-2-12-2-11i3−i311-1i3−i3-22000000001-1-110-11i3−i30i3−i30000001-1−i3i30000−i3i300000000
χ472-2-22-222-2-2200-2222-2-2-2-222002-2-222-22-2200-2-2200-22000000002-2-220-2200000000000-220000000000000000
χ482-2-22-222-2-2200-2222-2-2-2-22200-222-22-22-2200-2-22002-200000000-222-20-22000000000002-20000000000000000
χ492-2-22-222-2-2200-222-111-2-2-12002-2-22-1-221-1−i3i311-1i3−i3-2200000000-111-101-1−i3i30i3−i30000001-1−i3i30000i3−i300000000
χ502-2-22-222-2-2200-222-111-2-2-12002-2-22-1-221-1i3−i311-1−i3i3-2200000000-111-101-1i3−i30−i3i30000001-1i3−i30000−i3i300000000
χ512-2-22-222-2-2200-222-111-2-2-1200-222-2-1-221-1−i3i311-1i3−i32-2000000001-1-1101-1−i3i30i3−i3000000-11i3−i30000−i3i300000000
χ522-2-22-222-2-2200-222-111-2-2-1200-222-2-1-221-1i3−i311-1−i3i32-2000000001-1-1101-1i3−i30−i3i3000000-11−i3i30000i3−i300000000
χ5344444444444444-2-2-2-2-2-2-2-24400001-2-2-2-2-2-2111-2-200000000000000-21111-211000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-400001-2-2-2-2221112200000000000000211-1-12-1-1000000000000000000000000
χ554444-4-444444-4-4-4-2-2-2-2-2-2-2-24-4000012222-2-21112200000000000000-2-1-1112-1-1000000000000000000000000
χ564444-4-44444-44-4-4-2-2-2-2-2-2-2-2-4400001222222111-2-2000000000000002-1-1-1-1-211000000000000000000000000
χ5744-4-40044-4-400004-2-224-42-40044-4-4-2000000-222000000000000-2-22200000000000000000000000000000000
χ5844-4-40044-4-400004-2-224-42-400-4-444-2000000-22200000000000022-2-200000000000000000000000000000000
χ5944-4-40044-4-40000-244-4-22-42000000-2000000-22200000000004i−4i000000000000000000000000000000−2i2i0000
χ6044-4-40044-4-40000-244-4-22-42000000-2000000-2220000000000−4i4i0000000000000000000000000000002i−2i0000
χ614-44-4004-44-400004-22-2-442-4004-44-4-20000002-22000000000000-22-2200000000000000000000000000000000
χ624-44-4004-44-400004-22-2-442-400-44-44-20000002-220000000000002-22-200000000000000000000000000000000
χ634-44-4004-44-40000-24-442-2-42000000-20000002-22000000004i−4i000000000000000000000000000000−2i2i000000
χ644-44-4004-44-40000-24-442-2-42000000-20000002-2200000000−4i4i0000000000000000000000000000002i−2i000000
χ654-4-444-44-4-44004-4-24-4-4224-2000000-2-224-40022-200000000000000000-2200000000000000000000000000000
χ664-4-444-44-4-44004-4-2-22222-2-20000001-22-22−2i32i3-1-11−2i32i30000000000000001-1i3−i30i3−i3000000000000000000000000
χ674-4-444-44-4-44004-4-2-22222-2-20000001-22-222i3−2i3-1-112i3−2i30000000000000001-1−i3i30−i3i3000000000000000000000000
χ684-4-44-444-4-4400-44-24-4-4224-2000000-22-2-440022-2000000000000000002-200000000000000000000000000000
χ694-4-44-444-4-4400-44-2-22222-2-200000012-22-2−2i32i3-1-112i3−2i3000000000000000-11i3−i30−i3i3000000000000000000000000
χ704-4-44-444-4-4400-44-2-22222-2-200000012-22-22i3−2i3-1-11−2i32i3000000000000000-11−i3i30i3−i3000000000000000000000000
χ71666666-3-3-3-366-3-300000000-3-3000000000000000000222200000000000000000220000000-1-1-1-1000000-1-100
χ72666666-3-3-3-366-3-300000000-3-3000000000000000000-2-2-2-200000000000000000-2-2000000011110000001100
χ73666666-3-3-3-3-6-6-3-30000000033000000000000000000222200000000000000000-2-20000000-1-1-1-10000001100
χ74666666-3-3-3-3-6-6-3-30000000033000000000000000000-2-2-2-2000000000000000002200000001111000000-1-100
χ756666-6-6-3-3-3-36-63300000000-3300000000000000000022-2-2000000000000000002-20000000-1-111000000-1100
χ766666-6-6-3-3-3-36-63300000000-33000000000000000000-2-22200000000000000000-22000000011-1-10000001-100
χ776666-6-6-3-3-3-3-6633000000003-300000000000000000022-2-200000000000000000-220000000-1-1110000001-100
χ786666-6-6-3-3-3-3-6633000000003-3000000000000000000-2-222000000000000000002-2000000011-1-1000000-1100
χ7988-8-80088-8-80000-4-4-44-444400000020000002-2-2000000000000000000000000000000000000000000000000
χ808-88-8008-88-80000-4-44-44-4440000002000000-22-2000000000000000000000000000000000000000000000000
χ811212-12-1200-6-66600000000000000000000000000000000004i−4i0000000000000000000000000000−2i2i0000000000
χ821212-12-1200-6-6660000000000000000000000000000000000−4i4i00000000000000000000000000002i−2i0000000000
χ8312-1212-1200-66-66000000000000000000000000000000004i−4i0000000000000000000000000000−2i2i000000000000
χ8412-1212-1200-66-6600000000000000000000000000000000−4i4i00000000000000000000000000002i−2i000000000000
χ8512-12-121212-12-666-600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-1212-666-6006-6000000000000000000000000000000000000000000000000000000000000000000000000

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