Finite Group Databasebeta

← Group #13137392

Character table — Group #13137392

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12223444466612121212412121212336666661212121236661212121212121212121212121212121212121212121222446666888812121212242424242424242424661212
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
χ5111111-1-111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ6111111-1-111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ7111111-1-111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ8111111-1-111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-1-12-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-1-12-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-122-12-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-100000000000000
χ12222222222222222222222-12-1-122-12-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000111100000000000000
χ13222222-2-222222222-2-2-2-2-22-122-1-12-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-1-1-1111111110000000000000000000000002-2-1-111
χ14222222-2-222222222-2-2-2-2-22-122-1-12-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-1-1-111111111000000000000000000000000-2211-1-1
χ15222222-2-222222222-2-2-2-2-2-12-1-122-121111-1-1-1-1-1-111-2-2-2-222-1-1-1-11111111122-2-2-1-1-1-10000111100000000000000
χ16222222-2-222222222-2-2-2-2-2-12-1-122-121111-1-1-1-1-1-111-2-2-2-222-1-1-1-111111111-2-22211110000-1-1-1-100000000000000
χ1722222-222-2222-2-2-2-2-222-2-22222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ1822222-222-2222-2-2-2-2-222-2-22-122-1-12-12222-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ1922222-222-2222-2-2-2-2-222-2-22-122-1-12-12222-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
χ2022222-222-2222-2-2-2-2-222-2-2-12-1-122-12-1-1-1-1-1-1-1-1111122-2-2-2-21111-1-1-1-111110000−i3−i3i3i30000−i3−i3i3i300000000000000
χ2122222-222-2222-2-2-2-2-222-2-2-12-1-122-12-1-1-1-1-1-1-1-1111122-2-2-2-21111-1-1-1-111110000i3i3−i3−i30000i3i3−i3−i300000000000000
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
χ2322222-2-2-2-2222-2-2-2-22-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-2-22211-1-11111111111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-22-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-2-22211-1-11111111111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-22-2-222-12-1-122-121111-1-1-1-111-1-1-2-222-2-211111111-1-1-1-10000−i3−i3i3i30000i3i3−i3−i300000000000000
χ2622222-2-2-2-2222-2-2-2-22-2-222-12-1-122-121111-1-1-1-111-1-1-2-222-2-211111111-1-1-1-10000i3i3−i3−i30000−i3−i3i3i300000000000000
χ2722-2-2202i−2i02-2-2000002i−2i00222-22-2-2-22i2i−2i−2i22-2-200002i−2i000000002i2i−2i−2i0000000000002−2−i2i2000022−2−2−i2−i2i2i2000000
χ2822-2-2202i−2i02-2-2000002i−2i00222-22-2-2-22i2i−2i−2i22-2-200002i−2i000000002i2i−2i−2i000000000000−22i2−i20000−2−222i2i2−i2−i2000000
χ2922-2-220−2i2i02-2-200000−2i2i00222-22-2-2-2−2i−2i2i2i22-2-20000−2i2i00000000−2i−2i2i2i0000000000002−2i2−i2000022−2−2i2i2−i2−i2000000
χ3022-2-220−2i2i02-2-200000−2i2i00222-22-2-2-2−2i−2i2i2i22-2-20000−2i2i00000000−2i−2i2i2i000000000000−22−i2i20000−2−222−i2−i2i2i2000000
χ312-22-22200-2-22-222-2-20000022-22-2-2-2200002-22-22-20000002-222-2-200000000002i−2i000000002i−2i2i−2i00000000000000
χ322-22-22200-2-22-222-2-20000022-22-2-2-2200002-22-22-20000002-222-2-20000000000−2i2i00000000−2i2i−2i2i00000000000000
χ332-22-22200-2-22-222-2-200000-121-1-2-2123−33−3-11-11-113−300002-2-1-1113−33−333−3−3002i−2i−i3i3−i3i30000−ii−ii00000000000000
χ342-22-22200-2-22-222-2-200000-121-1-2-2123−33−3-11-11-113−300002-2-1-1113−33−333−3−300−2i2ii3−i3i3−i30000i−ii−i00000000000000
χ352-22-22200-2-22-222-2-200000-121-1-2-212−33−33-11-11-11−3300002-2-1-111−33−33−3−333002i−2ii3−i3i3−i30000−ii−ii00000000000000
χ362-22-22200-2-22-222-2-200000-121-1-2-212−33−33-11-11-11−3300002-2-1-111−33−33−3−33300−2i2i−i3i3−i3i30000i−ii−i00000000000000
χ372-22-22-2002-22-2-2-2220000022-22-2-2-2200002-22-2-22000000-22-2-222000000002-2002-2-220000000000000000000000
χ382-22-22-2002-22-2-2-2220000022-22-2-2-2200002-22-2-22000000-22-2-22200000000-2200-222-20000000000000000000000
χ392-22-22-2002-22-2-2-22200000-121-1-2-2123−33−3-11-111-1−330000-2211-1-13−33−3−3−3332-200-111-100003−3−3300000000000000
χ402-22-22-2002-22-2-2-22200000-121-1-2-2123−33−3-11-111-1−330000-2211-1-13−33−3−3−333-22001-1-110000−333−300000000000000
χ412-22-22-2002-22-2-2-22200000-121-1-2-212−33−33-11-111-13−30000-2211-1-1−33−3333−3−32-200-111-10000−333−300000000000000
χ422-22-22-2002-22-2-2-22200000-121-1-2-212−33−33-11-111-13−30000-2211-1-1−33−3333−3−3-22001-1-1100003−3−3300000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ44444444-4-444444444-4-4-4-4-4-2-2-2-2-2-2-2-222221111-2-2222222-2-21111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4544444-444-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-211112222-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4644444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-22222111122-2-222-2-222-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4744-4-4404i−4i04-4-4000004i−4i004-24-4-22-424i4i−4i−4i-2-2220000−2i2i00000000−2i−2i2i2i0000000000000000000000000000000000
χ4844-4-4404i−4i04-4-4000004i−4i00-24-224-42-4−2i−2i2i2i-2-22200004i−4i00000000−2i−2i2i2i0000000000000000000000000000000000
χ4944-4-4404i−4i04-4-4000004i−4i00-2-2-22-2222−2i−2i2i2i11-1-10000−2i2i00003i−3i3i−3iii−i−i3-33-3000000000000000000000000000000
χ5044-4-4404i−4i04-4-4000004i−4i00-2-2-22-2222−2i−2i2i2i11-1-10000−2i2i0000−3i3i−3i3iii−i−i-33-33000000000000000000000000000000
χ5144-4-440−4i4i04-4-400000−4i4i004-24-4-22-42−4i−4i4i4i-2-22200002i−2i000000002i2i−2i−2i0000000000000000000000000000000000
χ5244-4-440−4i4i04-4-400000−4i4i00-24-224-42-42i2i−2i−2i-2-2220000−4i4i000000002i2i−2i−2i0000000000000000000000000000000000
χ5344-4-440−4i4i04-4-400000−4i4i00-2-2-22-22222i2i−2i−2i11-1-100002i−2i00003i−3i3i−3i−i−iii-33-33000000000000000000000000000000
χ5444-4-440−4i4i04-4-400000−4i4i00-2-2-22-22222i2i−2i−2i11-1-100002i−2i0000−3i3i−3i3i−i−iii3-33-3000000000000000000000000000000
χ554-44-44400-4-44-444-4-4000004-2-4422-4-20000-22-224-4000000-22-2-22200000000000000000000000000000000000000
χ564-44-44400-4-44-444-4-400000-2-22-2222-223−2323−231-11-1-2223−230000-2211-1-1−33−33−3−333000000000000000000000000000000
χ574-44-44400-4-44-444-4-400000-2-22-2222-2−2323−23231-11-1-22−23230000-2211-1-13−33−333−3−3000000000000000000000000000000
χ584-44-44-4004-44-4-4-444000004-2-4422-4-20000-22-22-440000002-222-2-200000000000000000000000000000000000000
χ594-44-44-4004-44-4-4-44400000-2-22-2222-223−2323−231-11-12-2−232300002-2-1-111−33−3333−3−3000000000000000000000000000000
χ604-44-44-4004-44-4-4-44400000-2-22-2222-2−2323−23231-11-12-223−2300002-2-1-1113−33−3−3−333000000000000000000000000000000
χ614-4-4440000-4-4400000000044-4-4-444-400004-4-440000000000000000000000000000000000000000000000000000
χ624-4-4440000-4-440000000004-2-4-42-2420000-222-200000023−23000000000023−23−2323000000000000000000000000000000
χ634-4-4440000-4-440000000004-2-4-42-2420000-222-2000000−23230000000000−232323−23000000000000000000000000000000
χ644-4-4440000-4-44000000000-2422-44-2-4−2i32i32i3−2i3-222-200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ654-4-4440000-4-44000000000-2422-44-2-42i3−2i3−2i32i3-222-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ664-4-4440000-4-44000000000-2-2222-2-22−2i32i32i3−2i31-1-1100000023−23003i−3i−3i3ii3−i3−i3i3−333−3000000000000000000000000000000
χ674-4-4440000-4-44000000000-2-2222-2-22−2i32i32i3−2i31-1-11000000−232300−3i3i3i−3ii3−i3−i3i33−3−33000000000000000000000000000000
χ684-4-4440000-4-44000000000-2-2222-2-222i3−2i3−2i32i31-1-1100000023−2300−3i3i3i−3i−i3i3i3−i3−333−3000000000000000000000000000000
χ694-4-4440000-4-44000000000-2-2222-2-222i3−2i3−2i32i31-1-11000000−2323003i−3i−3i3i−i3i3i3−i33−3−33000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-1000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000000000000-2-2-2-2000011111111000000
χ726666-36-6-66-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000000022-2-20000-1-1-1-11111000000
χ736666-36-6-66-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000-2-22200001111-1-1-1-1000000
χ746666-3-666-6-3-3-33333-6-3-3330000000000000000000000000000000000000000000000000000003−33−33−33−3000000
χ756666-3-666-6-3-3-33333-6-3-333000000000000000000000000000000000000000000000000000000−33−33−33−33000000
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
χ7866-6-6-306i−6i0-33333−3333−330−3i3i−3i33i300000000000000000000000000000000000000000000002−2−i2i20000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ7966-6-6-306i−6i0-33333−3333−330−3i3i−3i33i30000000000000000000000000000000000000000000000−22i2−i20000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ8066-6-6-306i−6i0-333−3333−33330−3i3i3i3−3i300000000000000000000000000000000000000000000002−2−i2i20000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ8166-6-6-306i−6i0-333−3333−33330−3i3i3i3−3i30000000000000000000000000000000000000000000000−22i2−i20000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ8266-6-6-30−6i6i0-33333−3333−3303i−3i3i3−3i300000000000000000000000000000000000000000000002−2i2−i20000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ8366-6-6-30−6i6i0-33333−3333−3303i−3i3i3−3i30000000000000000000000000000000000000000000000−22−i2i20000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ8466-6-6-30−6i6i0-333−3333−333303i−3i−3i33i300000000000000000000000000000000000000000000002−2i2−i20000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ8566-6-6-30−6i6i0-333−3333−333303i−3i−3i33i30000000000000000000000000000000000000000000000−22−i2i20000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ8612-1212-12-61200-126-66-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-6-1200126-6666-6-60000000000000000000000000000000000000000000000000000000000000000000000000
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.