Finite Group Databasebeta

← Group #13137343

Character table — Group #13137343

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
χ511111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
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
χ132222222-2-2222-2-2-2-2-222-2-22222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-222-2-22-122-1-1-12-1-1-1-1-1-1-1-1-2-2221111-2-21111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ152222222-2-2222-2-2-2-2-222-2-22-122-1-1-12-1-1-1-1-1-1-1-1-2-2221111-2-21111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ162222222-2-2222-2-2-2-2-222-2-2-12-1-1222-12222-1-1-1-111-1-1-2-2-2-2111111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ172222222-2-2222-2-2-2-2-222-2-2-12-1-1222-12222-1-1-1-111-1-1-2-2-2-2111111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
χ1822222-2-2222222222-2-2-2-2-22-122-1-1-121111-1-1-1-122-2-2-1-111-2-2-1-1-1-11111111122-2-20000-1-1-1-1111100000000000000
χ1922222-2-2222222222-2-2-2-2-22-122-1-1-121111-1-1-1-122-2-2-1-111-2-2-1-1-1-111111111-2-22200001111-1-1-1-100000000000000
χ2022222-2-2222222222-2-2-2-2-2-12-1-1222-1-2-2-2-2-1-1-1-1-1-11122-2-211-1-1-1-1111111110000000000000000000000002-2-1-111
χ2122222-2-2222222222-2-2-2-2-2-12-1-1222-1-2-2-2-2-1-1-1-1-1-11122-2-211-1-1-1-111111111000000000000000000000000-2211-1-1
χ2222222-2-2-2-2222-2-2-2-22-2-22222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222-2-2-2-2222-2-2-2-22-2-2222-122-1-1-121111-1-1-1-1-2-2-2-211-1-12211111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ2422222-2-2-2-2222-2-2-2-22-2-2222-122-1-1-121111-1-1-1-1-2-2-2-211-1-12211111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ2522222-2-2-2-2222-2-2-2-22-2-222-12-1-1222-1-2-2-2-2-1-1-1-11111-2-222-1-111111111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2622222-2-2-2-2222-2-2-2-22-2-222-12-1-1222-1-2-2-2-2-1-1-1-11111-2-222-1-111111111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2722-2-222-2002-2-2000002-200222-22-2-2-222-2-222-2-2002-2000000000022-2-2000000002−22−20000000022−2−222−2−2000000
χ2822-2-222-2002-2-2000002-200222-22-2-2-222-2-222-2-2002-2000000000022-2-200000000−22−2200000000−2−222−2−222000000
χ2922-2-22-22002-2-200000-2200222-22-2-2-2-2-22222-2-200-220000000000-2-222000000002−2−220000000022−2−2−2−222000000
χ3022-2-22-22002-2-200000-2200222-22-2-2-2-2-22222-2-200-220000000000-2-22200000000−222−200000000−2−22222−2−2000000
χ312-22-22002-2-22-222-2-20000022-22-22-2-200002-22-22-2002-2000022-2-2000000002-20000002-22-2000000000000000000
χ322-22-22002-2-22-222-2-20000022-22-22-2-200002-22-22-2002-2000022-2-200000000-22000000-22-22000000000000000000
χ332-22-22002-2-22-222-2-2000002-1-221-11-23−33−3-11-112-200-113−300-1-1113−33−333−3−32-2000000-11-113−33−300000000000000
χ342-22-22002-2-22-222-2-2000002-1-221-11-23−33−3-11-112-200-113−300-1-1113−33−333−3−3-220000001-11-1−33−3300000000000000
χ352-22-22002-2-22-222-2-2000002-1-221-11-2−33−33-11-112-200-11−3300-1-111−33−33−3−3332-2000000-11-11−33−3300000000000000
χ362-22-22002-2-22-222-2-2000002-1-221-11-2−33−33-11-112-200-11−3300-1-111−33−33−3−333-220000001-11-13−33−300000000000000
χ372-22-2200-22-22-2-2-2220000022-22-22-2-200002-22-2-2200-220000-2-22200000000002i−2i000000002i−2i−2i2i00000000000000
χ382-22-2200-22-22-2-2-2220000022-22-22-2-200002-22-2-2200-220000-2-2220000000000−2i2i00000000−2i2i2i−2i00000000000000
χ392-22-2200-22-22-2-2-222000002-1-221-11-23−33−3-11-11-22001-1−330011-1-13−33−3−3−333002i−2i0000−i3i3i3−i3−iii−i00000000000000
χ402-22-2200-22-22-2-2-222000002-1-221-11-23−33−3-11-11-22001-1−330011-1-13−33−3−3−33300−2i2i0000i3−i3−i3i3i−i−ii00000000000000
χ412-22-2200-22-22-2-2-222000002-1-221-11-2−33−33-11-11-22001-13−30011-1-1−33−3333−3−3002i−2i0000i3−i3−i3i3−iii−i00000000000000
χ422-22-2200-22-22-2-2-222000002-1-221-11-2−33−33-11-11-22001-13−30011-1-1−33−3333−3−300−2i2i0000−i3i3i3−i3i−i−ii00000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ444444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-2111122-2-2222222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4544444-4-4444444444-4-4-4-4-4-2-2-2-2-2-2-2-222221111-2-222-2-222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4644444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-222221111222222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4744-4-444-4004-4-4000004-4004-24-4-222-4-2-222-2-222004-40000000000-2-2220000000000000000000000000000000000
χ4844-4-444-4004-4-4000004-400-24-224-4-4244-4-4-2-22200-220000000000-2-2220000000000000000000000000000000000
χ4944-4-444-4004-4-4000004-400-2-2-22-2222-2-22211-1-100-220000003i−3i3i−3i11-1-13i−3i3i−3i000000000000000000000000000000
χ5044-4-444-4004-4-4000004-400-2-2-22-2222-2-22211-1-100-22000000−3i3i−3i3i11-1-1−3i3i−3i3i000000000000000000000000000000
χ5144-4-44-44004-4-400000-44004-24-4-222-422-2-2-2-22200-44000000000022-2-20000000000000000000000000000000000
χ5244-4-44-44004-4-400000-4400-24-224-4-42-4-444-2-222002-2000000000022-2-20000000000000000000000000000000000
χ5344-4-44-44004-4-400000-4400-2-2-22-222222-2-211-1-1002-20000003i−3i3i−3i-1-111−3i3i−3i3i000000000000000000000000000000
χ5444-4-44-44004-4-400000-4400-2-2-22-222222-2-211-1-1002-2000000−3i3i−3i3i-1-1113i−3i3i−3i000000000000000000000000000000
χ554-44-44004-4-44-444-4-400000-242-2-44-420000-22-22-22004-40000-2-22200000000000000000000000000000000000000
χ564-44-44004-4-44-444-4-400000-2-22-22-22223−2323−231-11-1-2200-2223−230011-1-1−33−33−3−333000000000000000000000000000000
χ574-44-44004-4-44-444-4-400000-2-22-22-222−2323−23231-11-1-2200-22−23230011-1-13−33−333−3−3000000000000000000000000000000
χ584-44-4400-44-44-4-4-44400000-242-2-44-420000-22-222-200-44000022-2-200000000000000000000000000000000000000
χ594-44-4400-44-44-4-4-44400000-2-22-22-22223−2323−231-11-12-2002-2−232300-1-111−33−3333−3−3000000000000000000000000000000
χ604-44-4400-44-44-4-4-44400000-2-22-22-222−2323−23231-11-12-2002-223−2300-1-1113−33−3−3−333000000000000000000000000000000
χ614-4-4440000-4-4400000000044-4-4-4-44400004-4-440000000000000000000000000000000000000000000000000000
χ624-4-4440000-4-440000000004-2-4-422-2423−23−2323-222-20000000000000023−23−23230000000000000000000000000000000000
χ634-4-4440000-4-440000000004-2-4-422-24−232323−23-222-200000000000000−232323−230000000000000000000000000000000000
χ644-4-4440000-4-44000000000-2422-4-44-20000-222-200000000−2i32i300000000−2i32i32i3−2i3000000000000000000000000000000
χ654-4-4440000-4-44000000000-2422-4-44-20000-222-2000000002i3−2i3000000002i3−2i3−2i32i3000000000000000000000000000000
χ664-4-4440000-4-44000000000-2-22222-2-223−23−23231-1-1100000000−2i32i33i−3i−3i3i−333−3i3−i3−i3i3000000000000000000000000000000
χ674-4-4440000-4-44000000000-2-22222-2-223−23−23231-1-11000000002i3−2i3−3i3i3i−3i−333−3−i3i3i3−i3000000000000000000000000000000
χ684-4-4440000-4-44000000000-2-22222-2-2−232323−231-1-1100000000−2i32i3−3i3i3i−3i3−3−33i3−i3−i3i3000000000000000000000000000000
χ694-4-4440000-4-44000000000-2-22222-2-2−232323−231-1-11000000002i3−2i33i−3i−3i3i3−3−33−i3i3i3−i3000000000000000000000000000000
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
χ8612-1212-12-60012-126-66-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-600-12126-6666-6-60000000000000000000000000000000000000000000000000000000000000000000000000
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.