Finite Group Databasebeta

← Group #13137361

Character table — Group #13137361

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222344446661212121241212121233666666121212123666121212121212121212121212121212121212121212122244666688881212121224242424242424244412121212
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
χ5111111-1-111111111-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ6111111-1-111111111-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ7111111-1-111111111-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ8111111-1-111111111-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-1-1-12-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-100000000000000
χ102222222222222222222222-122-1-1-12-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000111100000000000000
χ11222222222222222222222-12-1-1222-12222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ12222222222222222222222-12-1-1222-12222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ13222222-2-222222222-2-2-2-2-22-122-1-1-121111-1-1-1-122-1-1-2-211-2-2-1-1-1-11111111122-2-2-1-1-1-10000111100000000000000
χ14222222-2-222222222-2-2-2-2-22-122-1-1-121111-1-1-1-122-1-1-2-211-2-2-1-1-1-111111111-2-22211110000-1-1-1-100000000000000
χ15222222-2-222222222-2-2-2-2-2-12-1-1222-1-2-2-2-2-1-1-1-1-1-12211-2-211-1-1-1-1111111110000000000000000000000002-2-1-111
χ16222222-2-222222222-2-2-2-2-2-12-1-1222-1-2-2-2-2-1-1-1-1-1-12211-2-211-1-1-1-111111111000000000000000000000000-2211-1-1
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
χ1822222-222-2222-2-2-2-2-222-2-22-122-1-1-12-1-1-1-1-1-1-1-1-2-2112211-2-21111-1-1-1-111110000−i3−i3i3i30000−i3−i3i3i300000000000000
χ1922222-222-2222-2-2-2-2-222-2-22-122-1-1-12-1-1-1-1-1-1-1-1-2-2112211-2-21111-1-1-1-111110000i3i3−i3−i30000i3i3−i3−i300000000000000
χ2022222-222-2222-2-2-2-2-222-2-2-12-1-1222-12222-1-1-1-111-2-2-1-1-2-2111111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ2122222-222-2222-2-2-2-2-222-2-2-12-1-1222-12222-1-1-1-111-2-2-1-1-2-2111111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
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
χ2322222-2-2-2-2222-2-2-2-22-2-2222-122-1-1-121111-1-1-1-1-2-211-2-2-1-12211111111-1-1-1-10000−i3−i3i3i30000i3i3−i3−i300000000000000
χ2422222-2-2-2-2222-2-2-2-22-2-2222-122-1-1-121111-1-1-1-1-2-211-2-2-1-12211111111-1-1-1-10000i3i3−i3−i30000−i3−i3i3i300000000000000
χ2522222-2-2-2-2222-2-2-2-22-2-222-12-1-1222-1-2-2-2-2-1-1-1-111-2-21122-1-111111111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2622222-2-2-2-2222-2-2-2-22-2-222-12-1-1222-1-2-2-2-2-1-1-1-111-2-21122-1-111111111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2722-2-22200-22-2-222-2-200000222-22-2-2-2000022-2-22-22-200000022-2-2000000002-2002-22-20000000000000000000000
χ2822-2-22200-22-2-222-2-200000222-22-2-2-2000022-2-22-22-200000022-2-200000000-2200-22-220000000000000000000000
χ2922-2-22200-22-2-222-2-2000002-12-2-111-233−3−3-1-1112-2-11003−300-1-11133−3−333−3−32-200-11-1100003−33−300000000000000
χ3022-2-22200-22-2-222-2-2000002-12-2-111-233−3−3-1-1112-2-11003−300-1-11133−3−333−3−3-22001-11-10000−33−3300000000000000
χ3122-2-22200-22-2-222-2-2000002-12-2-111-2−3−333-1-1112-2-1100−3300-1-111−3−333−3−3332-200-11-110000−33−3300000000000000
χ3222-2-22200-22-2-222-2-2000002-12-2-111-2−3−333-1-1112-2-1100−3300-1-111−3−333−3−333-22001-11-100003−33−300000000000000
χ3322-2-22-20022-2-2-2-22200000222-22-2-2-2000022-2-2-22-22000000-2-22200000000002i−2i000000002i−2i−2i2i00000000000000
χ3422-2-22-20022-2-2-2-22200000222-22-2-2-2000022-2-2-22-22000000-2-2220000000000−2i2i00000000−2i2i2i−2i00000000000000
χ3522-2-22-20022-2-2-2-222000002-12-2-111-233−3−3-1-111-221-100−330011-1-133−3−3−3−333002i−2i−i3i3i3−i30000−iii−i00000000000000
χ3622-2-22-20022-2-2-2-222000002-12-2-111-233−3−3-1-111-221-100−330011-1-133−3−3−3−33300−2i2ii3−i3−i3i30000i−i−ii00000000000000
χ3722-2-22-20022-2-2-2-222000002-12-2-111-2−3−333-1-111-221-1003−30011-1-1−3−33333−3−3002i−2ii3−i3−i3i30000−iii−i00000000000000
χ3822-2-22-20022-2-2-2-222000002-12-2-111-2−3−333-1-111-221-1003−30011-1-1−3−33333−3−300−2i2i−i3i3i3−i30000i−i−ii00000000000000
χ392-22-2202-20-22-2000002-20022-22-2-22-22-22-22-22-200002-2000000002-22-2000000000000−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2000000
χ402-22-2202-20-22-2000002-20022-22-2-22-22-22-22-22-200002-2000000002-22-2000000000000i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2000000
χ412-22-220-220-22-200000-220022-22-2-22-2-22-222-22-20000-2200000000-22-22000000000000−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2000000
χ422-22-220-220-22-200000-220022-22-2-22-2-22-222-22-20000-2200000000-22-22000000000000i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ44444444-4-444444444-4-4-4-4-4-2-2-2-2-2-2-2-222221111-2-2-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
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
χ4644444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-222221111222222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4744-4-44400-44-4-444-4-400000-24-224-4-420000-2-222-224-4000000-2-22200000000000000000000000000000000000000
χ4844-4-44400-44-4-444-4-400000-2-2-22-22222323−23−2311-1-1-22-220023−230011-1-1−3−333−3−333000000000000000000000000000000
χ4944-4-44400-44-4-444-4-400000-2-2-22-2222−23−23232311-1-1-22-2200−23230011-1-133−3−333−3−3000000000000000000000000000000
χ5044-4-44-40044-4-4-4-44400000-24-224-4-420000-2-2222-2-4400000022-2-200000000000000000000000000000000000000
χ5144-4-44-40044-4-4-4-44400000-2-2-22-22222323−23−2311-1-12-22-200−232300-1-111−3−33333−3−3000000000000000000000000000000
χ5244-4-44-40044-4-4-4-44400000-2-2-22-2222−23−23232311-1-12-22-20023−2300-1-11133−3−3−3−333000000000000000000000000000000
χ534-44-4404-40-44-4000004-4004-2-4422-2-4-22-22-22-2200004-400000000-22-220000000000000000000000000000000000
χ544-44-4404-40-44-4000004-400-242-2-4-4424-44-4-22-220000-2200000000-22-220000000000000000000000000000000000
χ554-44-4404-40-44-4000004-400-2-22-222-22-22-221-11-10000-2200003i−3i3i−3i1-11-13i−3i3i−3i000000000000000000000000000000
χ564-44-4404-40-44-4000004-400-2-22-222-22-22-221-11-10000-220000−3i3i−3i3i1-11-1−3i3i−3i3i000000000000000000000000000000
χ574-44-440-440-44-400000-44004-2-4422-2-42-22-2-22-220000-44000000002-22-20000000000000000000000000000000000
χ584-44-440-440-44-400000-4400-242-2-4-442-44-44-22-2200002-2000000002-22-20000000000000000000000000000000000
χ594-44-440-440-44-400000-4400-2-22-222-222-22-21-11-100002-200003i−3i3i−3i-11-11−3i3i−3i3i000000000000000000000000000000
χ604-44-440-440-44-400000-4400-2-22-222-222-22-21-11-100002-20000−3i3i−3i3i-11-113i−3i3i−3i000000000000000000000000000000
χ614-4-4440000-4-4400000000044-4-4-44-4400004-4-440000000000000000000000000000000000000000000000000000
χ624-4-4440000-4-440000000004-2-4-42-22423−23−2323-222-20000000000000023−23−23230000000000000000000000000000000000
χ634-4-4440000-4-440000000004-2-4-42-224−232323−23-222-200000000000000−232323−230000000000000000000000000000000000
χ644-4-4440000-4-44000000000-2422-44-4-20000-222-200000000−2i32i300000000−2i32i32i3−2i3000000000000000000000000000000
χ654-4-4440000-4-44000000000-2422-44-4-20000-222-2000000002i3−2i3000000002i3−2i3−2i32i3000000000000000000000000000000
χ664-4-4440000-4-44000000000-2-2222-22-223−23−23231-1-1100000000−2i32i33i−3i−3i3i−333−3i3−i3−i3i3000000000000000000000000000000
χ674-4-4440000-4-44000000000-2-2222-22-223−23−23231-1-11000000002i3−2i3−3i3i3i−3i−333−3−i3i3i3−i3000000000000000000000000000000
χ684-4-4440000-4-44000000000-2-2222-22-2−232323−231-1-1100000000−2i32i3−3i3i3i−3i3−3−33i3−i3−i3i3000000000000000000000000000000
χ694-4-4440000-4-44000000000-2-2222-22-2−232323−231-1-11000000002i3−2i33i−3i−3i3i3−3−33−i3i3i3−i3000000000000000000000000000000
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
χ786-66-6-306-603-3333−3333−330-3333−330000000000000000000000000000000000000000000000−i2i2−i2i20000ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ796-66-6-306-603-3333−3333−330-3333−330000000000000000000000000000000000000000000000i2−i2i2−i20000−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ806-66-6-306-603-33−3333−33330-33−33330000000000000000000000000000000000000000000000−i2i2−i2i20000ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ816-66-6-306-603-33−3333−33330-33−33330000000000000000000000000000000000000000000000i2−i2i2−i20000−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ826-66-6-30-6603-3333−3333−3303-3−33330000000000000000000000000000000000000000000000−i2i2i2−i20000ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ836-66-6-30-6603-3333−3333−3303-3−33330000000000000000000000000000000000000000000000i2−i2−i2i20000−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ846-66-6-30-6603-33−3333−333303-333−330000000000000000000000000000000000000000000000−i2i2i2−i20000ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ856-66-6-30-6603-33−3333−333303-333−330000000000000000000000000000000000000000000000i2−i2−i2i20000−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ861212-12-12-61200-12-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-6-120012-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000
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.