Finite Group Databasebeta

← Group #13137321

Character table — Group #13137321

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222344446664121212121212336666661212121212121212366612121212121212121212121212121212121212122244666688881212121224242424242424244412121212
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
χ5111111-1-11111-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ6111111-1-11111-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ7111111-1-11111-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ8111111-1-11111-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
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
χ13222222-2-22222-222-2-2-2-22-1222-1-1-122111122-1-1-1-1-1-1-2-2-2-211-1-1-1-11111111122-2-2-1-1-1-10000111100000000000000
χ14222222-2-22222-222-2-2-2-22-1222-1-1-122111122-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111-2-22211110000-1-1-1-100000000000000
χ15222222-2-22222-222-2-2-2-2-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1221111-2-2-1-1-1-1111111110000000022-2-20000-1-1-1-11111000000
χ16222222-2-22222-222-2-2-2-2-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1221111-2-2-1-1-1-11111111100000000-2-22200001111-1-1-1-1000000
χ1722222-222-2222-2-2-222-2-222222222-2-22222-2-22222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ1822222-222-2222-2-2-222-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-11122-2-2111111-1-1-1-111110000−i3−i3i3i30000−i3−i3i3i300000000000000
χ1922222-222-2222-2-2-222-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-11122-2-2111111-1-1-1-111110000i3i3−i3−i30000i3i3−i3−i300000000000000
χ2022222-222-2222-2-2-222-2-2-12-1-1-122211222211-1-1-1-1-2-2-1-111-2-21111-1-1-1-11111000000000000000033−3−333−3−3000000
χ2122222-222-2222-2-2-222-2-2-12-1-1-122211222211-1-1-1-1-2-2-1-111-2-21111-1-1-1-111110000000000000000−3−333−3−333000000
χ2222222-2-2-2-22222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222-2-2-2-22222-2-2-2-2222-1222-1-1-1-2-21111-2-2-1-1-1-111-2-222-1-111111111-1-1-1-10000−i3−i3i3i30000i3i3−i3−i300000000000000
χ2422222-2-2-2-22222-2-2-2-2222-1222-1-1-1-2-21111-2-2-1-1-1-111-2-222-1-111111111-1-1-1-10000i3i3−i3−i30000−i3−i3i3i300000000000000
χ2522222-2-2-2-22222-2-2-2-222-12-1-1-122211-2-2-2-211-1-1-1-1-2-211-1-12211111111-1-1-1-1000000000000000033−3−3−3−333000000
χ2622222-2-2-2-22222-2-2-2-222-12-1-1-122211-2-2-2-211-1-1-1-1-2-211-1-12211111111-1-1-1-10000000000000000−3−33333−3−3000000
χ2722-2-22200-22-2-202-20000222-2-22-2-2220000-2-222-2-22-200000022-2-2000000002-2002-22-20000000000000000000000
χ2822-2-22200-22-2-202-20000222-2-22-2-2220000-2-222-2-22-200000022-2-200000000-2200-22-220000000000000000000000
χ2922-2-22200-22-2-202-200002-12-2-2-1112233−3−3-2-2-1-111-1100003−3-1-11133−3−333−3−32-200-11-1100003−33−300000000000000
χ3022-2-22200-22-2-202-200002-12-2-2-1112233−3−3-2-2-1-111-1100003−3-1-11133−3−333−3−3-22001-11-10000−33−3300000000000000
χ3122-2-22200-22-2-202-200002-12-2-2-11122−3−333-2-2-1-111-110000−33-1-111−3−333−3−3332-200-11-110000−33−3300000000000000
χ3222-2-22200-22-2-202-200002-12-2-2-11122−3−333-2-2-1-111-110000−33-1-111−3−333−3−333-22001-11-100003−33−300000000000000
χ3322-2-22-20022-2-20-220000222-2-22-2-2-2-200002222-2-2-22000000-2-22200000000002i−2i000000002i−2i−2i2i00000000000000
χ3422-2-22-20022-2-20-220000222-2-22-2-2-2-200002222-2-2-22000000-2-2220000000000−2i2i00000000−2i2i2i−2i00000000000000
χ3522-2-22-20022-2-20-2200002-12-2-2-111-2-233−3−322-1-1111-10000−3311-1-133−3−3−3−333002i−2i−i3i3i3−i30000−iii−i00000000000000
χ3622-2-22-20022-2-20-2200002-12-2-2-111-2-233−3−322-1-1111-10000−3311-1-133−3−3−3−33300−2i2ii3−i3−i3i30000i−i−ii00000000000000
χ3722-2-22-20022-2-20-2200002-12-2-2-111-2-2−3−33322-1-1111-100003−311-1-1−3−33333−3−3002i−2ii3−i3−i3i30000−iii−i00000000000000
χ3822-2-22-20022-2-20-2200002-12-2-2-111-2-2−3−33322-1-1111-100003−311-1-1−3−33333−3−300−2i2i−i3i3i3−i30000i−i−ii00000000000000
χ392-22-2202-20-22-20002-20022-22-2-2-22002-22-2002-22-2002-2000000002-22-2000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000
χ402-22-2202-20-22-20002-20022-22-2-2-22002-22-2002-22-2002-2000000002-22-2000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000
χ412-22-2202-20-22-20002-200-121-11-2-223−32-22-23−3-11-1100-113−3003−33−3-11-113−33−300000000−i2i2−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ422-22-2202-20-22-20002-200-121-11-2-223−32-22-23−3-11-1100-113−3003−33−3-11-113−33−300000000i2−i2i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ432-22-2202-20-22-20002-200-121-11-2-22−332-22-2−33-11-1100-11−3300−33−33-11-11−33−3300000000−i2i2−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ442-22-2202-20-22-20002-200-121-11-2-22−332-22-2−33-11-1100-11−3300−33−33-11-11−33−3300000000i2−i2i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ452-22-220-220-22-2000-220022-22-2-2-2200-22-22002-22-200-2200000000-22-22000000000000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2000000
χ462-22-220-220-22-2000-220022-22-2-2-2200-22-22002-22-200-2200000000-22-22000000000000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2000000
χ472-22-220-220-22-2000-2200-121-11-2-223−3-22-223−3-11-11001-1−33003−33−31-11-1−33−3300000000−i2i2i2−i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ482-22-220-220-22-2000-2200-121-11-2-223−3-22-223−3-11-11001-1−33003−33−31-11-1−33−3300000000i2−i2−i2i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ492-22-220-220-22-2000-2200-121-11-2-22−33-22-22−33-11-11001-13−300−33−331-11-13−33−300000000−i2i2i2−i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ502-22-220-220-22-2000-2200-121-11-2-22−33-22-22−33-11-11001-13−300−33−331-11-13−33−300000000i2−i2−i2i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
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
χ52444444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-22222-2-21111-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5344444-444-4444-4-4-444-4-4-2-2-2-2-2-2-2-222-2-2-2-222111122-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ5444444-4-4-4-44444-4-4-4-444-2-2-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ5544-4-44400-44-4-404-40000-24-2224-4-4-2-2000022-2-2224-4000000-2-22200000000000000000000000000000000000000
χ5644-4-44400-44-4-404-40000-2-2-222-222-2-22323−23−232211-1-1-22000023−2311-1-1−3−333−3−333000000000000000000000000000000
χ5744-4-44400-44-4-404-40000-2-2-222-222-2-2−23−2323232211-1-1-220000−232311-1-133−3−333−3−3000000000000000000000000000000
χ5844-4-44-40044-4-40-440000-24-2224-4-4220000-2-2-2-222-4400000022-2-200000000000000000000000000000000000000
χ5944-4-44-40044-4-40-440000-2-2-222-222222323−23−23-2-211-1-12-20000−2323-1-111−3−33333−3−3000000000000000000000000000000
χ6044-4-44-40044-4-40-440000-2-2-222-22222−23−232323-2-211-1-12-2000023−23-1-11133−3−3−3−333000000000000000000000000000000
χ614-44-4404-40-44-40004-4004-2-44-422-200-22-2200-22-22004-400000000-22-220000000000000000000000000000000000
χ624-44-4404-40-44-40004-400-2-22-2222-223−23-22-2223−231-11-100-2223−2300−33−331-11-1−33−33000000000000000000000000000000
χ634-44-4404-40-44-40004-400-2-22-2222-2−2323-22-22−23231-11-100-22−2323003−33−31-11-13−33−3000000000000000000000000000000
χ644-44-440-440-44-4000-44004-2-44-422-2002-22-200-22-2200-44000000002-22-20000000000000000000000000000000000
χ654-44-440-440-44-4000-4400-2-22-2222-223−232-22-223−231-11-1002-2−232300−33−33-11-113−33−3000000000000000000000000000000
χ664-44-440-440-44-4000-4400-2-22-2222-2−23232-22-2−23231-11-1002-223−23003−33−3-11-11−33−33000000000000000000000000000000
χ674-4-4440000-4-44000000044-4-44-44-4000000004-4-4400000000000000000000000000000000000000000000000000
χ684-4-4440000-4-4400000004-2-4-442-220023−23−232300-222-200000000000023−23−23230000000000000000000000000000000000
χ694-4-4440000-4-4400000004-2-4-442-2200−232323−2300-222-2000000000000−232323−230000000000000000000000000000000000
χ704-4-4440000-4-440000000-2422-2-44-423−230000−2323-222-20000000023−23−232300000000000000000000000000000000000000
χ714-4-4440000-4-440000000-2422-2-44-4−2323000023−23-222-200000000−232323−2300000000000000000000000000000000000000
χ724-4-4440000-4-440000000-2-222-22-2223−2323−23−2323−23231-1-1100000000−333−3−333−33-3-33000000000000000000000000000000
χ734-4-4440000-4-440000000-2-222-22-2223−23−232323−23−23231-1-1100000000−333−33−3−33-333-3000000000000000000000000000000
χ744-4-4440000-4-440000000-2-222-22-22−232323−23−232323−231-1-11000000003−3−33−333−3-333-3000000000000000000000000000000
χ754-4-4440000-4-440000000-2-222-22-22−2323−232323−2323−231-1-11000000003−3−333−3−333-3-33000000000000000000000000000000
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
χ786666-36-6-66-3-3-3-6-3-3333300000000000000000000000000000000000000000000000000000000000000002-2-1-111
χ796666-36-6-66-3-3-3-6-3-333330000000000000000000000000000000000000000000000000000000000000000-2211-1-1
χ806666-3-666-6-3-3-3-633-3-333000000000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3
χ816666-3-666-6-3-3-3-633-3-333000000000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3
χ826666-3-6-6-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3
χ836666-3-6-6-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3
χ841212-12-12-61200-12-6660-6600000000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12-6-120012-66606-600000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-6012-1206-66000-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-60-121206-660006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-6000066-600000−6i36i30000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-6000066-6000006i3−6i30000000000000000000000000000000000000000000000000000000000000000000000

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