Finite Group Databasebeta

← Group #13137429

Character table — Group #13137429

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222344446661212121241212121233666666121212123666121212121212121212121212121212121212121212124444888812121212121212122424242424242424226666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111-1-111111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222222-1222-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-1222-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-1222-1-1-1-2-2-2-2-1-1-1-11122-2-2-1-1111111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-1222-1-1-1-2-2-2-2-1-1-1-11122-2-2-1-1111111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-1-12221111-1-1-1-1-2-2-1-11122-2-21111-1-1-1-11111000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-1-12221111-1-1-1-1-2-2-1-11122-2-21111-1-1-1-111110000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-2-2-222-2-22-1222-1-1-12222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1111111110000000000000000000000002-2-1-111
χ1922222-2-222222-2-2-2-2-222-2-22-1222-1-1-12222-1-1-1-1-1-1-2-2-2-21111-1-1-1-111111111000000000000000000000000-2211-1-1
χ2022222-2-222222-2-2-2-2-222-2-2-12-1-1-1222-1-1-1-1-1-1-1-1221111-2-2-2-2-1-1-1-111111111000022-2-200000000-1-1-1-11111000000
χ2122222-2-222222-2-2-2-2-222-2-2-12-1-1-1222-1-1-1-1-1-1-1-1221111-2-2-2-2-1-1-1-1111111110000-2-222000000001111-1-1-1-1000000
χ2222222-2-2-2-2222-2-2-2-22-2-22222222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222-2-2-2-2222-2-2-2-22-2-2222-1222-1-1-1-2-2-2-2-1-1-1-111-2-22211-1-111111111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-22-2-2222-1222-1-1-1-2-2-2-2-1-1-1-111-2-22211-1-111111111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-22-2-222-12-1-1-12221111-1-1-1-1-2-211-1-1-2-22211111111-1-1-1-1000000000000000033−3−3−3−333000000
χ2622222-2-2-2-2222-2-2-2-22-2-222-12-1-1-12221111-1-1-1-1-2-211-1-1-2-22211111111-1-1-1-10000000000000000−3−33333−3−3000000
χ2722-2-222-2002-2-222-2-200000222-2-22-2-2000022-2-2002-2002-200000022-2-200000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2000000
χ2822-2-222-2002-2-222-2-200000222-2-22-2-2000022-2-2002-2002-200000022-2-200000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2000000
χ2922-2-222-2002-2-222-2-200000-12-1112-2-23−33−3-1-11100-113−32-20033−3−3-1-11133−3−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ3022-2-222-2002-2-222-2-200000-12-1112-2-23−33−3-1-11100-113−32-20033−3−3-1-11133−3−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ3122-2-222-2002-2-222-2-200000-12-1112-2-2−33−33-1-11100-11−332-200−3−333-1-111−3−3330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ3222-2-222-2002-2-222-2-200000-12-1112-2-2−33−33-1-11100-11−332-200−3−333-1-111−3−3330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ3322-2-22-22002-2-2-2-22200000222-2-22-2-2000022-2-200-2200-22000000-2-22200000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i2000000
χ3422-2-22-22002-2-2-2-22200000222-2-22-2-2000022-2-200-2200-22000000-2-22200000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i2000000
χ3522-2-22-22002-2-2-2-22200000-12-1112-2-23−33−3-1-111001-1−33-220033−3−311-1-1−3−3330000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ3622-2-22-22002-2-2-2-22200000-12-1112-2-23−33−3-1-111001-1−33-220033−3−311-1-1−3−3330000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ3722-2-22-22002-2-2-2-22200000-12-1112-2-2−33−33-1-111001-13−3-2200−3−33311-1-133−3−30000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ3822-2-22-22002-2-2-2-22200000-12-1112-2-2−33−33-1-111001-13−3-2200−3−33311-1-133−3−30000i2−i2−i2i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ392-22-22002-2-22-2000002-20022-22-2-22-222-2-22-22-22-2000000002-22-200000000002i−2i000000002i2i−2i−2i00000000000000
χ402-22-22002-2-22-2000002-20022-22-2-22-222-2-22-22-22-2000000002-22-20000000000−2i2i00000000−2i−2i2i2i00000000000000
χ412-22-2200-22-22-200000-220022-22-2-22-2-2-2222-22-2-2200000000-22-22000000002-200000022-2-2000000000000000000
χ422-22-2200-22-22-200000-220022-22-2-22-2-2-2222-22-2-2200000000-22-2200000000-22000000-2-222000000000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-22222111122-2-222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4544444-4-444444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-2-2222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4644444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-2222211112222-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4744-4-444-4004-4-444-4-4000004-24-4-4-2220000-2-222004-400-22000000-2-2220000000000000000000000000000000000
χ4844-4-444-4004-4-444-4-400000-2-2-222-22223−2323−2311-1-100-2223−23-2200−3−33311-1-1−3−333000000000000000000000000000000
χ4944-4-444-4004-4-444-4-400000-2-2-222-222−2323−232311-1-100-22−2323-220033−3−311-1-133−3−3000000000000000000000000000000
χ5044-4-44-44004-4-4-4-444000004-24-4-4-2220000-2-22200-44002-200000022-2-20000000000000000000000000000000000
χ5144-4-44-44004-4-4-4-44400000-2-2-222-22223−2323−2311-1-1002-2−23232-200−3−333-1-11133−3−3000000000000000000000000000000
χ5244-4-44-44004-4-4-4-44400000-2-2-222-222−2323−232311-1-1002-223−232-20033−3−3-1-111−3−333000000000000000000000000000000
χ534-44-44004-4-44-4000004-4004-2-44-42-2244-4-4-22-22-2200000000-22-2200000000000000000000000000000000000000
χ544-44-44004-4-44-4000004-400-242-22-44-4-2-222-22-224-400000000-22-2200000000000000000000000000000000000000
χ554-44-44004-4-44-4000004-400-2-22-222-22-2-2221-11-1-22000000001-11-13i−3i3i−3i3i−3i3i−3i000000000000000000000000000000
χ564-44-44004-4-44-4000004-400-2-22-222-22-2-2221-11-1-22000000001-11-1−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000
χ574-44-4400-44-44-400000-44004-2-44-42-22-4-444-22-222-2000000002-22-200000000000000000000000000000000000000
χ584-44-4400-44-44-400000-4400-242-22-44-422-2-2-22-22-44000000002-22-200000000000000000000000000000000000000
χ594-44-4400-44-44-400000-4400-2-22-222-2222-2-21-11-12-200000000-11-113i−3i3i−3i−3i3i−3i3i000000000000000000000000000000
χ604-44-4400-44-44-400000-4400-2-22-222-2222-2-21-11-12-200000000-11-11−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000
χ614-4-4440000-4-4400000000044-4-44-4-4400004-4-440000000000000000000000000000000000000000000000000000
χ624-4-4440000-4-440000000004-2-4-4422-20000-222-200000000−2i32i300000000−2i32i32i3−2i3000000000000000000000000000000
χ634-4-4440000-4-440000000004-2-4-4422-20000-222-2000000002i3−2i3000000002i3−2i3−2i32i3000000000000000000000000000000
χ644-4-4440000-4-44000000000-2422-2-4-4423−23−2323-222-2000000000023−23−232300000000000000000000000000000000000000
χ654-4-4440000-4-44000000000-2422-2-4-44−232323−23-222-20000000000−232323−2300000000000000000000000000000000000000
χ664-4-4440000-4-44000000000-2-222-222-223−23−23231-1-1100000000−2i32i3−333−33i−3i−3i3ii3−i3−i3i3000000000000000000000000000000
χ674-4-4440000-4-44000000000-2-222-222-223−23−23231-1-11000000002i3−2i3−333−3−3i3i3i−3i−i3i3i3−i3000000000000000000000000000000
χ684-4-4440000-4-44000000000-2-222-222-2−232323−231-1-1100000000−2i32i33−3−33−3i3i3i−3ii3−i3−i3i3000000000000000000000000000000
χ694-4-4440000-4-44000000000-2-222-222-2−232323−231-1-11000000002i3−2i33−3−333i−3i−3i3i−i3i3i3−i3000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-100000000000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-200001111111100000000000000
χ726666-366-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000000000
χ736666-366-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000000000
χ746666-3-6-666-3-3-33333-6-3-3330000000000000000000000000000000000000022-2-20000-1-1-1-1111100000000000000
χ756666-3-6-666-3-3-33333-6-3-33300000000000000000000000000000000000000-2-22200001111-1-1-1-100000000000000
χ766666-3-6-6-6-6-3-3-33333633-3-30000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i300000000000000
χ776666-3-6-6-6-6-3-3-33333633-3-30000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i300000000000000
χ786-66-6-3006-63-3333−3333−330-3333−3300000000000000000000000000000000000000002i−2i0000−i3i3i3−i3−i−iii00000000000000
χ796-66-6-3006-63-3333−3333−330-3333−330000000000000000000000000000000000000000−2i2i0000i3−i3−i3i3ii−i−i00000000000000
χ806-66-6-3006-63-33−3333−33330-33−333300000000000000000000000000000000000000002i−2i0000i3−i3−i3i3−i−iii00000000000000
χ816-66-6-3006-63-33−3333−33330-33−33330000000000000000000000000000000000000000−2i2i0000−i3i3i3−i3ii−i−i00000000000000
χ826-66-6-300-663-3333−3333−3303-3−3333000000000000000000000000000000000000002-2000000-1-1113−3−3300000000000000
χ836-66-6-300-663-3333−3333−3303-3−333300000000000000000000000000000000000000-2200000011-1-1−333−300000000000000
χ846-66-6-300-663-33−3333−333303-333−33000000000000000000000000000000000000002-2000000-1-111−333−300000000000000
χ856-66-6-300-663-33−3333−333303-333−3300000000000000000000000000000000000000-2200000011-1-13−3−3300000000000000
χ861212-12-12-612-1200-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-6-121200-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-6000066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-6000066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.