Finite Group Databasebeta

← Group #13137438

Character table — Group #13137438

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12223444466612121212412121212336666661212121236661212121212121212121212121212121212121212121244448888121212121212121224242424242424244412121212
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
χ511111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222222-1222-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-1222-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-2222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-1222-1-1-1-2-2-2-2-1-1-1-122-2-2-1-111111111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-1222-1-1-1-2-2-2-2-1-1-1-122-2-2-1-111111111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-1-12221111-1-1-1-1-1-11122-2-2-2-21111-1-1-1-11111000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-1-12221111-1-1-1-1-1-11122-2-2-2-21111-1-1-1-111110000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-2-2-222-2-22-1222-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1-1-1111111110000000000000000000000002-2-1-111
χ1922222-2-222222-2-2-2-2-222-2-22-1222-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1-1-111111111000000000000000000000000-2211-1-1
χ2022222-2-222222-2-2-2-2-222-2-2-12-1-1-1222-1-1-1-1-1-1-1-11111-2-2-2-222-1-1-1-111111111000022-2-200000000-1-1-1-11111000000
χ2122222-2-222222-2-2-2-2-222-2-2-12-1-1-1222-1-1-1-1-1-1-1-11111-2-2-2-222-1-1-1-1111111110000-2-222000000001111-1-1-1-1000000
χ2222222-2-2-2-2222-2-2-2-22-2-22222222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222-2-2-2-2222-2-2-2-22-2-2222-1222-1-1-1-2-2-2-2-1-1-1-1-2-22211-1-11111111111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-22-2-2222-1222-1-1-1-2-2-2-2-1-1-1-1-2-22211-1-11111111111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-22-2-222-12-1-1-12221111-1-1-1-111-1-1-2-222-2-211111111-1-1-1-1000000000000000033−3−3−3−333000000
χ2622222-2-2-2-2222-2-2-2-22-2-222-12-1-1-12221111-1-1-1-111-1-1-2-222-2-211111111-1-1-1-10000000000000000−3−33333−3−3000000
χ2722-2-222-2002-2-222-2-200000222-2-22-2-2000022-2-22-2002-20000000022-2-2000000002−22−2000000002−22−22−22−2000000
χ2822-2-222-2002-2-222-2-200000222-2-22-2-2000022-2-22-2002-20000000022-2-200000000−22−2200000000−22−22−22−22000000
χ2922-2-222-2002-2-222-2-200000-12-1112-2-23−33−3-1-111-113−32-2000033−3−3-1-11133−3−300002−22−200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ3022-2-222-2002-2-222-2-200000-12-1112-2-23−33−3-1-111-113−32-2000033−3−3-1-11133−3−30000−22−2200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ3122-2-222-2002-2-222-2-200000-12-1112-2-2−33−33-1-111-11−332-20000−3−333-1-111−3−33300002−22−200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ3222-2-222-2002-2-222-2-200000-12-1112-2-2−33−33-1-111-11−332-20000−3−333-1-111−3−3330000−22−2200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ3322-2-22-22002-2-2-2-22200000222-2-22-2-2000022-2-2-2200-2200000000-2-222000000002−2−22000000002−22−2−22−22000000
χ3422-2-22-22002-2-2-2-22200000222-2-22-2-2000022-2-2-2200-2200000000-2-22200000000−222−200000000−22−222−22−2000000
χ3522-2-22-22002-2-2-2-22200000-12-1112-2-23−33−3-1-1111-1−33-22000033−3−311-1-1−3−33300002−2−2200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ3622-2-22-22002-2-2-2-22200000-12-1112-2-23−33−3-1-1111-1−33-22000033−3−311-1-1−3−3330000−222−200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ3722-2-22-22002-2-2-2-22200000-12-1112-2-2−33−33-1-1111-13−3-220000−3−33311-1-133−3−300002−2−2200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ3822-2-22-22002-2-2-2-22200000-12-1112-2-2−33−33-1-1111-13−3-220000−3−33311-1-133−3−30000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ392-2-222002-2-22-2000002-20022-22-2-2-2222-2-22-22-2000000002-22-22-2000000002i−2i0000002i2i−2i−2i000000000000000000
χ402-2-222002-2-22-2000002-20022-22-2-2-2222-2-22-22-2000000002-22-22-200000000−2i2i000000−2i−2i2i2i000000000000000000
χ412-2-22200-22-22-200000-220022-22-2-2-22-2-2222-22-200000000-22-22-2200000000002-20000000022-2-200000000000000
χ422-2-22200-22-22-200000-220022-22-2-2-22-2-2222-22-200000000-22-22-220000000000-2200000000-2-22200000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221111-2-222-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4544444-4-444444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-2111122222222-2-21111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4644444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-22222111122-2-222-2-222-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4744-4-444-4004-4-444-4-4000004-24-4-4-2220000-2-2224-400-2200000000-2-2220000000000000000000000000000000000
χ4844-4-444-4004-4-444-4-400000-2-2-222-22223−2323−2311-1-1-2223−23-220000−3−33311-1-1−3−333000000000000000000000000000000
χ4944-4-444-4004-4-444-4-400000-2-2-222-222−2323−232311-1-1-22−2323-22000033−3−311-1-133−3−3000000000000000000000000000000
χ5044-4-44-44004-4-4-4-444000004-24-4-4-2220000-2-222-44002-20000000022-2-20000000000000000000000000000000000
χ5144-4-44-44004-4-4-4-44400000-2-2-222-22223−2323−2311-1-12-2−23232-20000−3−333-1-11133−3−3000000000000000000000000000000
χ5244-4-44-44004-4-4-4-44400000-2-2-222-222−2323−232311-1-12-223−232-2000033−3−3-1-111−3−333000000000000000000000000000000
χ534-44-440000-4-4400000000044-4-44-44-400004-4-440000000000000000000000000000000000000000000000000000
χ544-44-440000-4-440000000004-2-4-442-220000-222-2000000−2i32i30000000000−2i32i3−2i32i3000000000000000000000000000000
χ554-44-440000-4-440000000004-2-4-442-220000-222-20000002i3−2i300000000002i3−2i32i3−2i3000000000000000000000000000000
χ564-44-440000-4-44000000000-2422-2-44-423−23−2323-222-2000000000023−23−232300000000000000000000000000000000000000
χ574-44-440000-4-44000000000-2422-2-44-4−232323−23-222-20000000000−232323−2300000000000000000000000000000000000000
χ584-44-440000-4-44000000000-2-222-22-2223−23−23231-1-11000000−2i32i300−333−33i−3i3i−3ii3−i3i3−i3000000000000000000000000000000
χ594-44-440000-4-44000000000-2-222-22-2223−23−23231-1-110000002i3−2i300−333−3−3i3i−3i3i−i3i3−i3i3000000000000000000000000000000
χ604-44-440000-4-44000000000-2-222-22-22−232323−231-1-11000000−2i32i3003−3−33−3i3i−3i3ii3−i3i3−i3000000000000000000000000000000
χ614-44-440000-4-44000000000-2-222-22-22−232323−231-1-110000002i3−2i3003−3−333i−3i3i−3i−i3i3−i3i3000000000000000000000000000000
χ624-4-444004-4-44-4000004-4004-2-44-422-244-4-4-22-2200000000-22-22-2200000000000000000000000000000000000000
χ634-4-444004-4-44-4000004-400-242-22-4-44-2-222-22-22000000004-4-22-2200000000000000000000000000000000000000
χ644-4-444004-4-44-4000004-400-2-22-2222-2-2-2221-11-100000000-221-11-13i−3i−3i3i3i−3i−3i3i000000000000000000000000000000
χ654-4-444004-4-44-4000004-400-2-22-2222-2-2-2221-11-100000000-221-11-1−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000
χ664-4-44400-44-44-400000-44004-2-44-422-2-4-444-22-22000000002-22-22-200000000000000000000000000000000000000
χ674-4-44400-44-44-400000-4400-242-22-4-4422-2-2-22-2200000000-442-22-200000000000000000000000000000000000000
χ684-4-44400-44-44-400000-4400-2-22-2222-222-2-21-11-1000000002-2-11-113i−3i−3i3i−3i3i3i−3i000000000000000000000000000000
χ694-4-44400-44-44-400000-4400-2-22-2222-222-2-21-11-1000000002-2-11-11−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000
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
χ786-6-66-3006-63-3333−3333−330-3333−33000000000000000000000000000000000000002i−2i000000−i−iii−i3i3i3−i300000000000000
χ796-6-66-3006-63-3333−3333−330-3333−3300000000000000000000000000000000000000−2i2i000000ii−i−ii3−i3−i3i300000000000000
χ806-6-66-3006-63-33−3333−33330-33−3333000000000000000000000000000000000000002i−2i000000−i−iiii3−i3−i3i300000000000000
χ816-6-66-3006-63-33−3333−33330-33−333300000000000000000000000000000000000000−2i2i000000ii−i−i−i3i3i3−i300000000000000
χ826-6-66-300-663-3333−3333−3303-3−333300000000000000000000000000000000000000002-200003−3−33-1-11100000000000000
χ836-6-66-300-663-3333−3333−3303-3−33330000000000000000000000000000000000000000-220000−333−311-1-100000000000000
χ846-6-66-300-663-33−3333−333303-333−3300000000000000000000000000000000000000002-20000−333−3-1-11100000000000000
χ856-6-66-300-663-33−3333−333303-333−330000000000000000000000000000000000000000-2200003−3−3311-1-100000000000000
χ861212-12-12-612-1200-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-6-121200-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-1212-12-6000066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-1212-12-6000066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000

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