Finite Group Databasebeta

← Group #13150858

Character table — Group #13150858

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12222236664466121212123366666666663666666666121212121212121212121212121212124444222244444466661212121266121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11-11-11-1-1-1-1-111111-11-11-11-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-11-11-1-1-1-11111-11-11-11-11
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-11-111111-1-1-1-11-11-1-11-11
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-11-11111-1-1-1-1-11-111-11-1
χ91111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11-111-1-11-1-1111-1-111-1-111-1-1-111-1
χ101111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11-1-1-111-111-111-1-111-1-1-1-1111-1-11
χ111111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111-1111-1-1-111-1-1-111-1-11111-1-11-1-11
χ121111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111-11-1-1111-1-11-1-111-1-111-1-111-111-1
χ131111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-111-1-1111-1-1-1-11111-1-11-1-11-1-111
χ141111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-11-111-1-1-111-1-11111-1-1-111-111-1-1
χ151111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1111-11-1-11-1-11111-1-1-1-1111-1-1111-1-1
χ161111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1111-1-111-111-1-111-1-1-1-111-111-1-1-111
χ172222222222222222222-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-100000000
χ182222222222222222222-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2000000001111111100000000
χ19222222222222222222-12-1222222-12-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000002222000000000000-1-1-1-1
χ20222222222222222222-12-1222222-12-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2-2-20000000000001111
χ212222222222-2-222-2-2-2-22-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-11111-2-2-2-2111111112222-2-2000000001111-1-1-1-100000000
χ222222222222-2-222-2-2-2-22-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-11111-2-2-2-211111111-2-2-2-22200000000-1-1-1-1111100000000
χ232222222222-2-222-2-2-2-2-12-1222222-12-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000002-22-2000000000000-11-11
χ242222222222-2-222-2-2-2-2-12-1222222-12-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000000-22-220000000000001-11-1
χ252222-2-222222-2-2-222-2-22-12-11111-12-12-1-2-2-1-11111-1-1-11122-2-2-1-1-1-1111122-2-22-200000000-1-111-1-11100000000
χ262222-2-222222-2-2-222-2-22-12-11111-12-12-1-2-2-1-11111-1-1-11122-2-2-1-1-1-11111-2-222-220000000011-1-111-1-100000000
χ272222-2-222222-2-2-222-2-2-12-12-2-2-2-22-12-1-111-1-11111-122-2-2-1-111-1-1-1-1111100000000002-2-220000000000001-1-11
χ282222-2-222222-2-2-222-2-2-12-12-2-2-2-22-12-1-111-1-11111-122-2-2-1-111-1-1-1-111110000000000-222-2000000000000-111-1
χ292222-2-22222-22-2-2-2-2222-12-11111-12-12-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-122-2-2-220000000011-1-1-1-11100000000
χ302222-2-22222-22-2-2-2-2222-12-11111-12-12-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-1-2-2222-200000000-1-11111-1-100000000
χ312222-2-22222-22-2-2-2-222-12-12-2-2-2-22-12-1-111-1-11111-1-2-22211-1-11111-1-1-1-1000000000022-2-200000000000011-1-1
χ322222-2-22222-22-2-2-2-222-12-12-2-2-2-22-12-1-111-1-11111-1-2-22211-1-11111-1-1-1-10000000000-2-222000000000000-1-111
χ3322-2-22-22-2-22002-20000222222-2-2-2-2-2-222-22-222-2-2-200000000000000002i−2i2i−2i000000000000002i−2i2i−2i00000000
χ3422-2-22-22-2-22002-20000222222-2-2-2-2-2-222-22-222-2-2-20000000000000000−2i2i−2i2i00000000000000−2i2i−2i2i00000000
χ3522-2-22-22-2-22002-200002-12-1-1-1111-21-2-12-2-11-1-11113−33−3000033−3−333−3−32i−2i2i−2i0000000000−i3i3−i3i3−ii−ii00000000
χ3622-2-22-22-2-22002-200002-12-1-1-1111-21-2-12-2-11-1-11113−33−3000033−3−333−3−3−2i2i−2i2i0000000000i3−i3i3−i3i−ii−i00000000
χ3722-2-22-22-2-22002-200002-12-1-1-1111-21-2-12-2-11-1-1111−33−330000−3−333−3−3332i−2i2i−2i0000000000i3−i3i3−i3−ii−ii00000000
χ3822-2-22-22-2-22002-200002-12-1-1-1111-21-2-12-2-11-1-1111−33−330000−3−333−3−333−2i2i−2i2i0000000000−i3i3−i3i3i−ii−i00000000
χ3922-2-2-222-2-2200-2200002222-2-222-2-2-2-22-222-2-2-222-200000000000000002i−2i−2i2i000000000000002i−2i−2i2i00000000
χ4022-2-2-222-2-2200-2200002222-2-222-2-2-2-22-222-2-2-222-20000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i00000000
χ4122-2-2-222-2-2200-2200002-12-111-1-11-21-2-1-22-1111-1-113−3−33000033−3−3−3−3332i−2i−2i2i0000000000−i3i3i3−i3−iii−i00000000
χ4222-2-2-222-2-2200-2200002-12-111-1-11-21-2-1-22-1111-1-113−3−33000033−3−3−3−333−2i2i2i−2i0000000000i3−i3−i3i3i−i−ii00000000
χ4322-2-2-222-2-2200-2200002-12-111-1-11-21-2-1-22-1111-1-11−333−30000−3−33333−3−32i−2i−2i2i0000000000i3−i3−i3i3−iii−i00000000
χ4422-2-2-222-2-2200-2200002-12-111-1-11-21-2-1-22-1111-1-11−333−30000−3−33333−3−3−2i2i2i−2i0000000000−i3i3i3−i3i−i−ii00000000
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-21-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ474444-4-444444-4-4-444-4-4-2-2-2-22222-2-2-2-212211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000
χ484444-4-44444-44-4-4-4-444-2-2-2-22222-2-2-2-212211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4944-4-44-44-4-44004-40000-24-2444-4-4-42-42-2-22-22-2-22220000000000000000000000000000000000000000000000
χ5044-4-44-44-4-44004-40000-2-2-2-2-2-22222221-221-111-1-1-123−2323−230000−3−333−3−333000000000000000000000000000000
χ5144-4-44-44-4-44004-40000-2-2-2-2-2-22222221-221-111-1-1-1−2323−2323000033−3−333−3−3000000000000000000000000000000
χ5244-4-4-444-4-4400-440000-24-24-4-444-42-42-22-2-2222-2-220000000000000000000000000000000000000000000000
χ5344-4-4-444-4-4400-440000-2-2-2-222-2-2222212-21-1-1-111-123−23−23230000−3−33333−3−3000000000000000000000000000000
χ5444-4-4-444-4-4400-440000-2-2-2-222-2-2222212-21-1-1-111-1−232323−23000033−3−3−3−333000000000000000000000000000000
χ554-44-4004-44-40000000044-4-400004-4-44400-4-4000040000000000000000000000000000000000000000000000
χ564-44-4004-44-4000000004-2-42−2i32i3−2i32i3-2-424-20022−2i32i3−2i32i3-20000000000000000000000000000000000000000000000
χ574-44-4004-44-4000000004-2-422i3−2i32i3−2i3-2-424-200222i3−2i32i3−2i3-20000000000000000000000000000000000000000000000
χ584-44-4004-44-400000000-242-4000042-4-2-200220000-2000000−2i32i30000−2i32i3−2i32i3000000000000000000000000000000
χ594-44-4004-44-400000000-242-4000042-4-2-200220000-20000002i3−2i300002i3−2i32i3−2i3000000000000000000000000000000
χ604-44-4004-44-400000000-2-222−2i32i3−2i32i3-222-2100-1-1i3−i3i3−i31000000−2i32i33-33-3i3−i3i3−i3000000000000000000000000000000
χ614-44-4004-44-400000000-2-222−2i32i3−2i32i3-222-2100-1-1i3−i3i3−i310000002i3−2i3-33-33−i3i3−i3i3000000000000000000000000000000
χ624-44-4004-44-400000000-2-2222i3−2i32i3−2i3-222-2100-1-1−i3i3−i3i31000000−2i32i3-33-33i3−i3i3−i3000000000000000000000000000000
χ634-44-4004-44-400000000-2-2222i3−2i32i3−2i3-222-2100-1-1−i3i3−i3i310000002i3−2i33-33-3−i3i3−i3i3000000000000000000000000000000
χ644-4-440044-4-40000000044-4-40000-444-4400-440000-40000000000000000000000000000000000000000000000
χ654-4-440044-4-4000000004-2-42−2i32i32i3−2i324-2-4-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000
χ664-4-440044-4-4000000004-2-422i3−2i3−2i32i324-2-4-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000
χ674-4-440044-4-400000000-242-40000-4-242-2002-200002000023−230023−23−23230000000000000000000000000000000000
χ684-4-440044-4-400000000-242-40000-4-242-2002-2000020000−232300−232323−230000000000000000000000000000000000
χ694-4-440044-4-400000000-2-222−2i32i32i3−2i32-2-22100-11i3−i3−i3i3-1000023−2300−333−33i−3i−3i3i000000000000000000000000000000
χ704-4-440044-4-400000000-2-222−2i32i32i3−2i32-2-22100-11i3−i3−i3i3-10000−2323003−3−33−3i3i3i−3i000000000000000000000000000000
χ714-4-440044-4-400000000-2-2222i3−2i3−2i32i32-2-22100-11−i3i3i3−i3-1000023−2300−333−3−3i3i3i−3i000000000000000000000000000000
χ724-4-440044-4-400000000-2-2222i3−2i3−2i32i32-2-22100-11−i3i3i3−i3-10000−2323003−3−333i−3i−3i3i000000000000000000000000000000
χ73666666-3-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000002222000000000000-1-1-1-10000
χ74666666-3-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000-2-2-2-200000000000011110000
χ75666666-3-3-3-3-6-6-3-33333000000000000000000000000000000000000000000002-22-2000000000000-11-110000
χ76666666-3-3-3-3-6-6-3-3333300000000000000000000000000000000000000000000-22-220000000000001-11-10000
χ776666-6-6-3-3-3-36-633-3-3330000000000000000000000000000000000000000000022-2-2000000000000-1-1110000
χ786666-6-6-3-3-3-36-633-3-33300000000000000000000000000000000000000000000-2-22200000000000011-1-10000
χ796666-6-6-3-3-3-3-663333-3-3000000000000000000000000000000000000000000002-2-22000000000000-111-10000
χ806666-6-6-3-3-3-3-663333-3-300000000000000000000000000000000000000000000-222-20000000000001-1-110000
χ811212-12-1212-12-666-600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-1212-666-6006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-1200-66-660000−6i36i30000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-1200-66-6600006i3−6i30000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-121200-6-66600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-121200-6-666000000−636300000000000000000000000000000000000000000000000000000000000000000000

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