Finite Group Databasebeta

← Group #13137416

Character table — Group #13137416

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122234444666121212124121212123366666612121212366612121212121212121212121212121212121212121212224466668888121212122424242424242424226666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
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
χ5111111-1-11111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ6111111-1-11111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ7111111-1-11111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ8111111-1-11111-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
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
χ11222222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000011111111000000
χ13222222-2-22222-2-2-2-2-222-2-22-1222-1-1-12222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1111111110000000000000000000000002-2-1-111
χ14222222-2-22222-2-2-2-2-222-2-22-1222-1-1-12222-1-1-1-1-1-1-2-2-2-21111-1-1-1-111111111000000000000000000000000-2211-1-1
χ15222222-2-22222-2-2-2-2-222-2-2-12-1-1-1222-1-1-1-1-1-1-1-1221111-2-2-2-2-1-1-1-1111111110000000022-2-20000-1-1-1-11111000000
χ16222222-2-22222-2-2-2-2-222-2-2-12-1-1-1222-1-1-1-1-1-1-1-1221111-2-2-2-2-1-1-1-11111111100000000-2-22200001111-1-1-1-1000000
χ1722222-222-22222222-2-2-2-2-222222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ1822222-222-22222222-2-2-2-2-22-1222-1-1-1-2-2-2-2-1-1-1-11122-2-2-1-1111111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ1922222-222-22222222-2-2-2-2-22-1222-1-1-1-2-2-2-2-1-1-1-11122-2-2-1-1111111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
χ2022222-222-22222222-2-2-2-2-2-12-1-1-12221111-1-1-1-1-2-2-1-11122-2-21111-1-1-1-11111000000000000000033−3−333−3−3000000
χ2122222-222-22222222-2-2-2-2-2-12-1-1-12221111-1-1-1-1-2-2-1-11122-2-21111-1-1-1-111110000000000000000−3−333−3−333000000
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
χ2722-2-22200-22-2-2000002-200222-2-22-2-222-2-222-2-22-20000000022-2-200000000002i−2i000000002i2i−2i−2i00000000000000
χ2822-2-22200-22-2-2000002-200222-2-22-2-222-2-222-2-22-20000000022-2-20000000000−2i2i00000000−2i−2i2i2i00000000000000
χ2922-2-22-20022-2-200000-2200222-2-22-2-2-2-22222-2-2-2200000000-2-222000000002-20022-2-20000000000000000000000
χ3022-2-22-20022-2-200000-2200222-2-22-2-2-2-22222-2-2-2200000000-2-22200000000-2200-2-2220000000000000000000000
χ312-2-22202-20-2-2222-2-20000022-22-2-22-200002-22-2002-2002-200000022-2-20000000000002−22−200002−22−22−22−2000000
χ322-2-22202-20-2-2222-2-20000022-22-2-22-200002-22-2002-2002-200000022-2-2000000000000−22−220000−22−22−22−22000000
χ332-2-22202-20-2-2222-2-200000-121-11-22-23−33−3-11-1100-113−32-2003−33−3-1-11133−3−3000000002−22−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ342-2-22202-20-2-2222-2-200000-121-11-22-23−33−3-11-1100-113−32-2003−33−3-1-11133−3−300000000−22−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ352-2-22202-20-2-2222-2-200000-121-11-22-2−33−33-11-1100-11−332-200−33−33-1-111−3−333000000002−22−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ362-2-22202-20-2-2222-2-200000-121-11-22-2−33−33-11-1100-11−332-200−33−33-1-111−3−33300000000−22−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ372-2-2220-220-2-22-2-2220000022-22-2-22-200002-22-200-2200-22000000-2-2220000000000002−2−2200002−22−2−22−22000000
χ382-2-2220-220-2-22-2-2220000022-22-2-22-200002-22-200-2200-22000000-2-222000000000000−222−20000−22−222−22−2000000
χ392-2-2220-220-2-22-2-22200000-121-11-22-23−33−3-11-11001-1−33-22003−33−311-1-1−3−333000000002−2−220000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ402-2-2220-220-2-22-2-22200000-121-11-22-23−33−3-11-11001-1−33-22003−33−311-1-1−3−33300000000−222−20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ412-2-2220-220-2-22-2-22200000-121-11-22-2−33−33-11-11001-13−3-2200−33−3311-1-133−3−3000000002−2−220000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ422-2-2220-220-2-22-2-22200000-121-11-22-2−33−33-11-11001-13−3-2200−33−3311-1-133−3−300000000−222−20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ44444444-4-44444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-2-2222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4544444-444-44444444-4-4-4-4-4-2-2-2-2-2-2-2-22222111122-2-222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000
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
χ4744-4-44400-44-4-4000004-4004-24-4-4-22244-4-4-2-222-2200000000-2-22200000000000000000000000000000000000000
χ4844-4-44400-44-4-4000004-400-24-2224-4-4-2-222-2-2224-400000000-2-22200000000000000000000000000000000000000
χ4944-4-44400-44-4-4000004-400-2-2-222-222-2-22211-1-1-220000000011-1-13i−3i3i−3i3i−3i3i−3i000000000000000000000000000000
χ5044-4-44400-44-4-4000004-400-2-2-222-222-2-22211-1-1-220000000011-1-1−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000
χ5144-4-44-40044-4-400000-44004-24-4-4-222-4-444-2-2222-20000000022-2-200000000000000000000000000000000000000
χ5244-4-44-40044-4-400000-4400-24-2224-4-422-2-2-2-222-440000000022-2-200000000000000000000000000000000000000
χ5344-4-44-40044-4-400000-4400-2-2-222-22222-2-211-1-12-200000000-1-1113i−3i3i−3i−3i3i−3i3i000000000000000000000000000000
χ5444-4-44-40044-4-400000-4400-2-2-222-22222-2-211-1-12-200000000-1-111−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000
χ554-44-440000-44-400000000044-4-44-4-4400004-4-440000000000000000000000000000000000000000000000000000
χ564-44-440000-44-40000000004-2-4-4422-20000-222-200000000−2i32i300000000−2i32i32i3−2i3000000000000000000000000000000
χ574-44-440000-44-40000000004-2-4-4422-20000-222-2000000002i3−2i3000000002i3−2i3−2i32i3000000000000000000000000000000
χ584-44-440000-44-4000000000-2422-2-4-4423−23−2323-222-2000000000023−23−232300000000000000000000000000000000000000
χ594-44-440000-44-4000000000-2422-2-4-44−232323−23-222-20000000000−232323−2300000000000000000000000000000000000000
χ604-44-440000-44-4000000000-2-222-222-223−23−23231-1-1100000000−2i32i3−333−33i−3i−3i3ii3−i3−i3i3000000000000000000000000000000
χ614-44-440000-44-4000000000-2-222-222-223−23−23231-1-11000000002i3−2i3−333−3−3i3i3i−3i−i3i3i3−i3000000000000000000000000000000
χ624-44-440000-44-4000000000-2-222-222-2−232323−231-1-1100000000−2i32i33−3−33−3i3i3i−3ii3−i3−i3i3000000000000000000000000000000
χ634-44-440000-44-4000000000-2-222-222-2−232323−231-1-11000000002i3−2i33−3−333i−3i−3i3i−i3i3i3−i3000000000000000000000000000000
χ644-4-44404-40-4-4444-4-4000004-2-44-42-220000-22-22004-400-22000000-2-2220000000000000000000000000000000000
χ654-4-44404-40-4-4444-4-400000-2-22-222-2223−2323−231-11-100-2223−23-2200−33−3311-1-1−3−333000000000000000000000000000000
χ664-4-44404-40-4-4444-4-400000-2-22-222-22−2323−23231-11-100-22−2323-22003−33−311-1-133−3−3000000000000000000000000000000
χ674-4-4440-440-4-44-4-444000004-2-44-42-220000-22-2200-44002-200000022-2-20000000000000000000000000000000000
χ684-4-4440-440-4-44-4-44400000-2-22-222-2223−2323−231-11-1002-2−23232-200−33−33-1-11133−3−3000000000000000000000000000000
χ694-4-4440-440-4-44-4-44400000-2-22-222-22−2323−23231-11-1002-223−232-2003−33−3-1-111−3−333000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002222-1-1-1-10000-1-1-1-100000000000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-211110000111100000000000000
χ726666-36-6-66-3-3-33333-6-3-3330000000000000000000000000000000000000022-2-2-1-1-1-10000111100000000000000
χ736666-36-6-66-3-3-33333-6-3-33300000000000000000000000000000000000000-2-22211110000-1-1-1-100000000000000
χ746666-3-666-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000−i3i3−i3i30000−i3i3−i3i300000000000000
χ756666-3-666-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000i3−i3i3−i30000i3−i3i3−i300000000000000
χ766666-3-6-6-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000−i3i3−i3i30000i3−i3i3−i300000000000000
χ776666-3-6-6-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000i3−i3i3−i30000−i3i3−i3i300000000000000
χ7866-6-6-3600-6-33333−3333−330-3333−3300000000000000000000000000000000000000002i−2i−i3i3i3−i30000−i−iii00000000000000
χ7966-6-6-3600-6-33333−3333−330-3333−330000000000000000000000000000000000000000−2i2ii3−i3−i3i30000ii−i−i00000000000000
χ8066-6-6-3600-6-333−3333−33330-33−333300000000000000000000000000000000000000002i−2ii3−i3−i3i30000−i−iii00000000000000
χ8166-6-6-3600-6-333−3333−33330-33−33330000000000000000000000000000000000000000−2i2i−i3i3i3−i30000ii−i−i00000000000000
χ8266-6-6-3-6006-33333−3333−3303-3−3333000000000000000000000000000000000000002-200-1-11100003−3−3300000000000000
χ8366-6-6-3-6006-33333−3333−3303-3−333300000000000000000000000000000000000000-220011-1-10000−333−300000000000000
χ8466-6-6-3-6006-333−3333−333303-333−33000000000000000000000000000000000000002-200-1-1110000−333−300000000000000
χ8566-6-6-3-6006-333−3333−333303-333−3300000000000000000000000000000000000000-220011-1-100003−3−3300000000000000
χ8612-1212-12-600006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-600006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-6012-12066-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-60-1212066-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000

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