Finite Group Databasebeta

← Group #13137402

Character table — Group #13137402

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
χ511111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ102222222222222222222222-122-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ11222222222222222222222-12-1-1222-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ12222222222222222222222-12-1-1222-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ132222222-2-2222-2-2-2-2-222-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-222-2-22-122-1-1-12-1-1-1-1-1-1-1-122-2-21111-2-21111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ152222222-2-2222-2-2-2-2-222-2-22-122-1-1-12-1-1-1-1-1-1-1-122-2-21111-2-21111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ162222222-2-2222-2-2-2-2-222-2-2-12-1-1222-12222-1-1-1-1-1-111-2-2-2-2111111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ172222222-2-2222-2-2-2-2-222-2-2-12-1-1222-12222-1-1-1-1-1-111-2-2-2-2111111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
χ1822222-2-2222222222-2-2-2-2-22-122-1-1-121111-1-1-1-1-2-2-2-2-1-11122-1-1-1-11111111122-2-20000-1-1-1-1111100000000000000
χ1922222-2-2222222222-2-2-2-2-22-122-1-1-121111-1-1-1-1-2-2-2-2-1-11122-1-1-1-111111111-2-22200001111-1-1-1-100000000000000
χ2022222-2-2222222222-2-2-2-2-2-12-1-1222-1-2-2-2-2-1-1-1-1111122-2-2-1-1-1-1-1-1111111110000000000000000000000002-2-1-111
χ2122222-2-2222222222-2-2-2-2-2-12-1-1222-1-2-2-2-2-1-1-1-1111122-2-2-1-1-1-1-1-111111111000000000000000000000000-2211-1-1
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
χ2322222-2-2-2-2222-2-2-2-22-2-2222-122-1-1-121111-1-1-1-1-2-22211-1-1-2-211111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ2422222-2-2-2-2222-2-2-2-22-2-2222-122-1-1-121111-1-1-1-1-2-22211-1-1-2-211111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ2522222-2-2-2-2222-2-2-2-22-2-222-12-1-1222-1-2-2-2-2-1-1-1-111-1-1-2-2221111111111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2622222-2-2-2-2222-2-2-2-22-2-222-12-1-1222-1-2-2-2-2-1-1-1-111-1-1-2-2221111111111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2722-2-222-2002-2-2000002-200222-22-2-2-222-2-222-2-22-200000000000022-2-2000000002−22−20000000022−2−222−2−2000000
χ2822-2-222-2002-2-2000002-200222-22-2-2-222-2-222-2-22-200000000000022-2-200000000−22−2200000000−2−222−2−222000000
χ2922-2-22-22002-2-200000-2200222-22-2-2-2-2-22222-2-2-22000000000000-2-222000000002−2−220000000022−2−2−2−222000000
χ3022-2-22-22002-2-200000-2200222-22-2-2-2-2-22222-2-2-22000000000000-2-22200000000−222−200000000−2−22222−2−2000000
χ312-2-222002-2-22-222-2-20000022-2-2-22-2200002-22-200002-2002-222-2-2000000002i−2i0000002i−2i2i−2i000000000000000000
χ322-2-222002-2-22-222-2-20000022-2-2-22-2200002-22-200002-2002-222-2-200000000−2i2i000000−2i2i−2i2i000000000000000000
χ332-2-222002-2-22-222-2-2000002-1-2-21-1123−33−3-11-110000-113−32-2-1-1113−33−333−3−32i−2i000000−ii−ii−i3i3−i3i300000000000000
χ342-2-222002-2-22-222-2-2000002-1-2-21-1123−33−3-11-110000-113−32-2-1-1113−33−333−3−3−2i2i000000i−ii−ii3−i3i3−i300000000000000
χ352-2-222002-2-22-222-2-2000002-1-2-21-112−33−33-11-110000-11−332-2-1-111−33−33−3−3332i−2i000000−ii−iii3−i3i3−i300000000000000
χ362-2-222002-2-22-222-2-2000002-1-2-21-112−33−33-11-110000-11−332-2-1-111−33−33−3−333−2i2i000000i−ii−i−i3i3−i3i300000000000000
χ372-2-22200-22-22-2-2-2220000022-2-2-22-2200002-22-20000-2200-22-2-22200000000002-2000000002-2-2200000000000000
χ382-2-22200-22-22-2-2-2220000022-2-2-22-2200002-22-20000-2200-22-2-2220000000000-2200000000-222-200000000000000
χ392-2-22200-22-22-2-2-222000002-1-2-21-1123−33−3-11-1100001-1−33-2211-1-13−33−3−3−333002-200003−3−33-111-100000000000000
χ402-2-22200-22-22-2-2-222000002-1-2-21-1123−33−3-11-1100001-1−33-2211-1-13−33−3−3−33300-220000−333−31-1-1100000000000000
χ412-2-22200-22-22-2-2-222000002-1-2-21-112−33−33-11-1100001-13−3-2211-1-1−33−3333−3−3002-20000−333−3-111-100000000000000
χ422-2-22200-22-22-2-2-222000002-1-2-21-112−33−33-11-1100001-13−3-2211-1-1−33−3333−3−300-2200003−3−331-1-1100000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ444444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-2-222222222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4544444-4-4444444444-4-4-4-4-4-2-2-2-2-2-2-2-2222211112222-2-222-2-21111-1-1-1-1-1-1-1-1000000000000000000000000000000
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
χ4744-4-444-4004-4-4000004-4004-24-4-222-4-2-222-2-2224-4000000000000-2-2220000000000000000000000000000000000
χ4844-4-444-4004-4-4000004-400-24-224-4-4244-4-4-2-222-22000000000000-2-2220000000000000000000000000000000000
χ4944-4-444-4004-4-4000004-400-2-2-22-2222-2-22211-1-1-22000000003i−3i3i−3i11-1-13i−3i3i−3i000000000000000000000000000000
χ5044-4-444-4004-4-4000004-400-2-2-22-2222-2-22211-1-1-2200000000−3i3i−3i3i11-1-1−3i3i−3i3i000000000000000000000000000000
χ5144-4-44-44004-4-400000-44004-24-4-222-422-2-2-2-222-4400000000000022-2-20000000000000000000000000000000000
χ5244-4-44-44004-4-400000-4400-24-224-4-42-4-444-2-2222-200000000000022-2-20000000000000000000000000000000000
χ5344-4-44-44004-4-400000-4400-2-2-22-222222-2-211-1-12-2000000003i−3i3i−3i-1-111−3i3i−3i3i000000000000000000000000000000
χ5444-4-44-44004-4-400000-4400-2-2-22-222222-2-211-1-12-200000000−3i3i−3i3i-1-1113i−3i3i−3i000000000000000000000000000000
χ554-44-440000-4-4400000000044-44-4-44-400004-4-440000000000000000000000000000000000000000000000000000
χ564-44-440000-4-440000000004-2-4422-2-423−23−2323-222-20000000000000023−23−23230000000000000000000000000000000000
χ574-44-440000-4-440000000004-2-4422-2-4−232323−23-222-200000000000000−232323−230000000000000000000000000000000000
χ584-44-440000-4-44000000000-242-2-4-4420000-222-200−2i32i300000000000000−2i32i32i3−2i3000000000000000000000000000000
χ594-44-440000-4-44000000000-242-2-4-4420000-222-2002i3−2i3000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ604-44-440000-4-44000000000-2-22-222-2223−23−23231-1-1100−2i32i30000003i−3i−3i3i−333−3i3−i3−i3i3000000000000000000000000000000
χ614-44-440000-4-44000000000-2-22-222-2223−23−23231-1-11002i3−2i3000000−3i3i3i−3i−333−3−i3i3i3−i3000000000000000000000000000000
χ624-44-440000-4-44000000000-2-22-222-22−232323−231-1-1100−2i32i3000000−3i3i3i−3i3−3−33i3−i3−i3i3000000000000000000000000000000
χ634-44-440000-4-44000000000-2-22-222-22−232323−231-1-11002i3−2i30000003i−3i−3i3i3−3−33−i3i3i3−i3000000000000000000000000000000
χ644-4-444004-4-44-444-4-400000-2422-44-4-20000-22-2200004-400-22-2-22200000000000000000000000000000000000000
χ654-4-444004-4-44-444-4-400000-2-2222-22-223−2323−231-11-10000-2223−23-2211-1-1−33−33−3−333000000000000000000000000000000
χ664-4-444004-4-44-444-4-400000-2-2222-22-2−2323−23231-11-10000-22−2323-2211-1-13−33−333−3−3000000000000000000000000000000
χ674-4-44400-44-44-4-4-44400000-2422-44-4-20000-22-220000-44002-222-2-200000000000000000000000000000000000000
χ684-4-44400-44-44-4-4-44400000-2-2222-22-223−2323−231-11-100002-2−23232-2-1-111−33−3333−3−3000000000000000000000000000000
χ694-4-44400-44-44-4-4-44400000-2-2222-22-2−2323−23231-11-100002-223−232-2-1-1113−33−3−3−333000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-1000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-20000000011111111000000
χ726666-366-6-6-3-3-33333-6-3-3330000000000000000000000000000000000000000000000000000003−33−33−33−3000000
χ736666-366-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000000000000000−33−33−33−33000000
χ746666-3-6-666-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-200000000-1-1-1-11111000000
χ756666-3-6-666-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222000000001111-1-1-1-1000000
χ766666-3-6-6-6-6-3-3-33333633-3-30000000000000000000000000000000000000000000000000000003−33−3−33−33000000
χ776666-3-6-6-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000000000000000−33−333−33−3000000
χ7866-6-6-36-600-33333−3333−330-3333−330000000000000000000000000000000000000000002−22−200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ7966-6-6-36-600-33333−3333−330-3333−33000000000000000000000000000000000000000000−22−2200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ8066-6-6-36-600-333−3333−33330-33−33330000000000000000000000000000000000000000002−22−200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ8166-6-6-36-600-333−3333−33330-33−3333000000000000000000000000000000000000000000−22−2200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ8266-6-6-3-6600-33333−3333−3303-3−33330000000000000000000000000000000000000000002−2−2200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ8366-6-6-3-6600-33333−3333−3303-3−3333000000000000000000000000000000000000000000−222−200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ8466-6-6-3-6600-333−3333−333303-333−330000000000000000000000000000000000000000002−2−2200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ8566-6-6-3-6600-333−3333−333303-333−33000000000000000000000000000000000000000000−222−200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ8612-1212-12-6000066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-6000066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-60012-126-66-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-600-12126-6666-6-60000000000000000000000000000000000000000000000000000000000000000000000000

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