Finite Group Databasebeta

← Group #13137431

Character table — Group #13137431

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12223444466641212121212123366666612121212121212123666121212121212121212121212121212121212121222446666888812121212242424242424242424661212
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
χ5111111-1-11111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ6111111-1-11111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ7111111-1-11111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ8111111-1-11111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ922222222222222222222-1222-1-1-122-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-100000000000000
χ1022222222222222222222-1222-1-1-122-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000111100000000000000
χ112222222222222222222-12-1-1-1222-1-12222-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-1000000
χ122222222222222222222-12-1-1-1222-1-12222-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000011111111000000
χ13222222-2-22222-2-2-2-2-2222-1222-1-1-122111122-1-1-1-1-1-1-2-2-2-211-1-1-1-11111111122-2-2-1-1-1-10000111100000000000000
χ14222222-2-22222-2-2-2-2-2222-1222-1-1-122111122-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111-2-22211110000-1-1-1-100000000000000
χ15222222-2-22222-2-2-2-2-222-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1221111-2-2-1-1-1-1111111110000000022-2-20000-1-1-1-11111000000
χ16222222-2-22222-2-2-2-2-222-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1221111-2-2-1-1-1-11111111100000000-2-22200001111-1-1-1-1000000
χ1722222-222-2222-222-2-2-2-222222222-2-22222-2-22222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ1822222-222-2222-222-2-2-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-11122-2-2111111-1-1-1-111110000−i3−i3i3i30000−i3−i3i3i300000000000000
χ1922222-222-2222-222-2-2-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-11122-2-2111111-1-1-1-111110000i3i3−i3−i30000i3i3−i3−i300000000000000
χ2022222-222-2222-222-2-2-2-2-12-1-1-122211222211-1-1-1-1-2-2-1-111-2-21111-1-1-1-11111000000000000000033−3−333−3−3000000
χ2122222-222-2222-222-2-2-2-2-12-1-1-122211222211-1-1-1-1-2-2-1-111-2-21111-1-1-1-111110000000000000000−3−333−3−333000000
χ2222222-2-2-2-22222-2-222-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222-2-2-2-22222-2-222-2-22-1222-1-1-1-2-21111-2-2-1-1-1-111-2-222-1-111111111-1-1-1-10000−i3−i3i3i30000i3i3−i3−i300000000000000
χ2422222-2-2-2-22222-2-222-2-22-1222-1-1-1-2-21111-2-2-1-1-1-111-2-222-1-111111111-1-1-1-10000i3i3−i3−i30000−i3−i3i3i300000000000000
χ2522222-2-2-2-22222-2-222-2-2-12-1-1-122211-2-2-2-211-1-1-1-1-2-211-1-12211111111-1-1-1-1000000000000000033−3−3−3−333000000
χ2622222-2-2-2-22222-2-222-2-2-12-1-1-122211-2-2-2-211-1-1-1-1-2-211-1-12211111111-1-1-1-10000000000000000−3−33333−3−3000000
χ2722-2-2202i−2i02-2-202i−2i0000222-2-22-2-2002i2i−2i−2i0022-2-2002i−2i000000002i2i−2i−2i0000000000002−2−i2i200002−22−2−i2i2−i2i2000000
χ2822-2-2202i−2i02-2-202i−2i0000222-2-22-2-2002i2i−2i−2i0022-2-2002i−2i000000002i2i−2i−2i000000000000−22i2−i20000−22−22i2−i2i2−i2000000
χ2922-2-2202i−2i02-2-202i−2i0000-12-1112-2-23−32i2i−2i−2i3−3-1-11100−ii−i3i30033−3−3−i−iii−i3−i3i3i3000000002−2−i2i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ3022-2-2202i−2i02-2-202i−2i0000-12-1112-2-23−32i2i−2i−2i3−3-1-11100−ii−i3i30033−3−3−i−iii−i3−i3i3i300000000−22i2−i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ3122-2-2202i−2i02-2-202i−2i0000-12-1112-2-2−332i2i−2i−2i−33-1-11100−iii3−i300−3−333−i−iiii3i3−i3−i3000000002−2−i2i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ3222-2-2202i−2i02-2-202i−2i0000-12-1112-2-2−332i2i−2i−2i−33-1-11100−iii3−i300−3−333−i−iiii3i3−i3−i300000000−22i2−i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ3322-2-220−2i2i02-2-20−2i2i0000222-2-22-2-200−2i−2i2i2i0022-2-200−2i2i00000000−2i−2i2i2i0000000000002−2i2−i200002−22−2i2−i2i2−i2000000
χ3422-2-220−2i2i02-2-20−2i2i0000222-2-22-2-200−2i−2i2i2i0022-2-200−2i2i00000000−2i−2i2i2i000000000000−22−i2i20000−22−22−i2i2−i2i2000000
χ3522-2-220−2i2i02-2-20−2i2i0000-12-1112-2-23−3−2i−2i2i2i3−3-1-11100i−ii3−i30033−3−3ii−i−ii3i3−i3−i3000000002−2i2−i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ3622-2-220−2i2i02-2-20−2i2i0000-12-1112-2-23−3−2i−2i2i2i3−3-1-11100i−ii3−i30033−3−3ii−i−ii3i3−i3−i300000000−22−i2i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ3722-2-220−2i2i02-2-20−2i2i0000-12-1112-2-2−33−2i−2i2i2i−33-1-11100i−i−i3i300−3−333ii−i−i−i3−i3i3i3000000002−2i2−i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ3822-2-220−2i2i02-2-20−2i2i0000-12-1112-2-2−33−2i−2i2i2i−33-1-11100i−i−i3i300−3−333ii−i−i−i3−i3i3i300000000−22−i2i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ392-22-22200-2-2-22000002-222-22-2-22-2220000-2-22-22-22-20000002-22-200000000002i−2i000000002i−2i2i−2i00000000000000
χ402-22-22200-2-2-22000002-222-22-2-22-2220000-2-22-22-22-20000002-22-20000000000−2i2i00000000−2i2i−2i2i00000000000000
χ412-22-22200-2-2-22000002-22-1-22-21-11223−33−3-2-2-11-11-1100003−3-11-113−33−33−33−3002i−2i−i3i3−i3i30000−ii−ii00000000000000
χ422-22-22200-2-2-22000002-22-1-22-21-11223−33−3-2-2-11-11-1100003−3-11-113−33−33−33−300−2i2ii3−i3i3−i30000i−ii−i00000000000000
χ432-22-22200-2-2-22000002-22-1-22-21-1122−33−33-2-2-11-11-110000−33-11-11−33−33−33−33002i−2ii3−i3i3−i30000−ii−ii00000000000000
χ442-22-22200-2-2-22000002-22-1-22-21-1122−33−33-2-2-11-11-110000−33-11-11−33−33−33−3300−2i2i−i3i3−i3i30000i−ii−i00000000000000
χ452-22-22-2002-2-2200000-2222-22-2-22-2-2-20000222-22-2-22000000-22-22000000002-2002-2-220000000000000000000000
χ462-22-22-2002-2-2200000-2222-22-2-22-2-2-20000222-22-2-22000000-22-2200000000-2200-222-20000000000000000000000
χ472-22-22-2002-2-2200000-222-1-22-21-11-2-23−33−322-11-111-10000−331-11-13−33−3−33−332-200-111-100003−3−3300000000000000
χ482-22-22-2002-2-2200000-222-1-22-21-11-2-23−33−322-11-111-10000−331-11-13−33−3−33−33-22001-1-110000−333−300000000000000
χ492-22-22-2002-2-2200000-222-1-22-21-11-2-2−33−3322-11-111-100003−31-11-1−33−333−33−32-200-111-10000−333−300000000000000
χ502-22-22-2002-2-2200000-222-1-22-21-11-2-2−33−3322-11-111-100003−31-11-1−33−333−33−3-22001-1-1100003−3−3300000000000000
χ514444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ52444444-4-44444-4-4-4-4-444-2-2-2-2-2-2-2-2-2-22222-2-21111-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5344444-444-4444-444-4-4-4-4-2-2-2-2-2-2-2-222-2-2-2-222111122-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ5444444-4-4-4-44444-4-444-4-4-2-2-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ5544-4-4404i−4i04-4-404i−4i00004-24-4-4-22200−2i−2i2i2i00-2-222004i−4i00000000−2i−2i2i2i0000000000000000000000000000000000
χ5644-4-4404i−4i04-4-404i−4i0000-2-2-222-22223−23−2i−2i2i2i23−2311-1-100−2i2i−2i32i300−3−333ii−i−ii3i3−i3−i3000000000000000000000000000000
χ5744-4-4404i−4i04-4-404i−4i0000-2-2-222-222−2323−2i−2i2i2i−232311-1-100−2i2i2i3−2i30033−3−3ii−i−i−i3−i3i3i3000000000000000000000000000000
χ5844-4-440−4i4i04-4-40−4i4i00004-24-4-4-222002i2i−2i−2i00-2-22200−4i4i000000002i2i−2i−2i0000000000000000000000000000000000
χ5944-4-440−4i4i04-4-40−4i4i0000-2-2-222-22223−232i2i−2i−2i23−2311-1-1002i−2i2i3−2i300−3−333−i−iii−i3−i3i3i3000000000000000000000000000000
χ6044-4-440−4i4i04-4-40−4i4i0000-2-2-222-222−23232i2i−2i−2i−232311-1-1002i−2i−2i32i30033−3−3−i−iiii3i3−i3−i3000000000000000000000000000000
χ614-44-44400-4-4-44000004-4-242-22-44-4-2-2000022-22-224-4000000-22-2200000000000000000000000000000000000000
χ624-44-44400-4-4-44000004-4-2-22-222-22-2-223−2323−23221-11-1-22000023−231-11-1−33−33−33−33000000000000000000000000000000
χ634-44-44400-4-4-44000004-4-2-22-222-22-2-2−2323−2323221-11-1-220000−23231-11-13−33−33−33−3000000000000000000000000000000
χ644-44-44-4004-4-4400000-44-242-22-44-4220000-2-2-22-22-440000002-22-200000000000000000000000000000000000000
χ654-44-44-4004-4-4400000-44-2-22-222-222223−2323−23-2-21-11-12-20000−2323-11-11−33−333−33−3000000000000000000000000000000
χ664-44-44-4004-4-4400000-44-2-22-222-2222−2323−2323-2-21-11-12-2000023−23-11-113−33−3−33−33000000000000000000000000000000
χ674-4-4440000-44-4000000044-4-44-4-44000000004-4-4400000000000000000000000000000000000000000000000000
χ684-4-4440000-44-400000004-2-4-4422-200−2i32i32i3−2i300-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ694-4-4440000-44-400000004-2-4-4422-2002i3−2i3−2i32i300-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ704-4-4440000-44-40000000-2422-2-4-4423−230000−2323-222-20000000023−23−232300000000000000000000000000000000000000
χ714-4-4440000-44-40000000-2422-2-4-44−2323000023−23-222-200000000−232323−2300000000000000000000000000000000000000
χ724-4-4440000-44-40000000-2-222-222-223−23−2i32i32i3−2i3−23231-1-1100000000−333−3i3−i3−i3i33i−3i−3i3i000000000000000000000000000000
χ734-4-4440000-44-40000000-2-222-222-223−232i3−2i3−2i32i3−23231-1-1100000000−333−3−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000
χ744-4-4440000-44-40000000-2-222-222-2−2323−2i32i32i3−2i323−231-1-11000000003−3−33i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000
χ754-4-4440000-44-40000000-2-222-222-2−23232i3−2i3−2i32i323−231-1-11000000003−3−33−i3i3i3−i33i−3i−3i3i000000000000000000000000000000
χ766666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000000000000000022-1-1-1-1
χ776666-36666-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000000000000000000-2-21111
χ786666-36-6-66-3-3-3-63333-3-300000000000000000000000000000000000000000000000000000000000000002-2-1-111
χ796666-36-6-66-3-3-3-63333-3-30000000000000000000000000000000000000000000000000000000000000000-2211-1-1
χ806666-3-666-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3
χ816666-3-666-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3
χ826666-3-6-6-6-6-3-3-3633-3-333000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3
χ836666-3-6-6-6-6-3-3-3633-3-333000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3
χ841212-12-12-6012i−12i0-6660−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12-60−12i12i0-66606i−6i00000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-61200-1266-600000-660000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-6-12001266-6000006-60000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-600006-6600063−63000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-600006-66000−6363000000000000000000000000000000000000000000000000000000000000000000000000

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