Finite Group Databasebeta

← Group #13137430

Character table — Group #13137430

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
χ511111-1-111111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
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
χ132222222-2-2222-222-2-2-2-222222222-2-22222-2-22222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-222-2-2-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-11122-2-2111111-1-1-1-111110000−i3−i3i3i30000−i3−i3i3i300000000000000
χ152222222-2-2222-222-2-2-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-11122-2-2111111-1-1-1-111110000i3i3−i3−i30000i3i3−i3−i300000000000000
χ162222222-2-2222-222-2-2-2-2-12-1-1-122211222211-1-1-1-1-2-2-1-111-2-21111-1-1-1-11111000000000000000033−3−333−3−3000000
χ172222222-2-2222-222-2-2-2-2-12-1-1-122211222211-1-1-1-1-2-2-1-111-2-21111-1-1-1-111110000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-2-2-2222-1222-1-1-122111122-1-1-1-1-1-1-2-2-2-211-1-1-1-11111111122-2-2-1-1-1-10000111100000000000000
χ1922222-2-222222-2-2-2-2-2222-1222-1-1-122111122-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111-2-22211110000-1-1-1-100000000000000
χ2022222-2-222222-2-2-2-2-222-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1221111-2-2-1-1-1-1111111110000000022-2-20000-1-1-1-11111000000
χ2122222-2-222222-2-2-2-2-222-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1221111-2-2-1-1-1-11111111100000000-2-22200001111-1-1-1-1000000
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
χ272-22-222-2002-2-202-20000222-2-2-2-220022-2-20022-2-2002-20000000022-2-2000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000
χ282-22-222-2002-2-202-20000222-2-2-2-220022-2-20022-2-2002-20000000022-2-2000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000
χ292-22-222-2002-2-202-20000-12-111-2-223−322-2-23−3-1-11100-113−30033−3−3-1-11133−3−300000000−i2i2−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ302-22-222-2002-2-202-20000-12-111-2-223−322-2-23−3-1-11100-113−30033−3−3-1-11133−3−300000000i2−i2i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ312-22-222-2002-2-202-20000-12-111-2-22−3322-2-2−33-1-11100-11−3300−3−333-1-111−3−33300000000−i2i2−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ322-22-222-2002-2-202-20000-12-111-2-22−3322-2-2−33-1-11100-11−3300−3−333-1-111−3−33300000000i2−i2i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ332-22-22-22002-2-20-220000222-2-2-2-2200-2-2220022-2-200-2200000000-2-222000000000000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2000000
χ342-22-22-22002-2-20-220000222-2-2-2-2200-2-2220022-2-200-2200000000-2-222000000000000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2000000
χ352-22-22-22002-2-20-220000-12-111-2-223−3-2-2223−3-1-111001-1−330033−3−311-1-1−3−33300000000−i2i2i2−i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ362-22-22-22002-2-20-220000-12-111-2-223−3-2-2223−3-1-111001-1−330033−3−311-1-1−3−33300000000i2−i2−i2i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ372-22-22-22002-2-20-220000-12-111-2-22−33-2-222−33-1-111001-13−300−3−33311-1-133−3−300000000−i2i2i2−i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ382-22-22-22002-2-20-220000-12-111-2-22−33-2-222−33-1-111001-13−300−3−33311-1-133−3−300000000i2−i2−i2i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ392-2-222002-2-2-22000002-222-22-22-2-2220000-2-22-22-22-20000002-22-200000000002i−2i000000002i−2i2i−2i00000000000000
χ402-2-222002-2-2-22000002-222-22-22-2-2220000-2-22-22-22-20000002-22-20000000000−2i2i00000000−2i2i−2i2i00000000000000
χ412-2-222002-2-2-22000002-22-1-22-2-111223−33−3-2-2-11-11-1100003−3-11-113−33−33−33−3002i−2i−i3i3−i3i30000−ii−ii00000000000000
χ422-2-222002-2-2-22000002-22-1-22-2-111223−33−3-2-2-11-11-1100003−3-11-113−33−33−33−300−2i2ii3−i3i3−i30000i−ii−i00000000000000
χ432-2-222002-2-2-22000002-22-1-22-2-11122−33−33-2-2-11-11-110000−33-11-11−33−33−33−33002i−2ii3−i3i3−i30000−ii−ii00000000000000
χ442-2-222002-2-2-22000002-22-1-22-2-11122−33−33-2-2-11-11-110000−33-11-11−33−33−33−3300−2i2i−i3i3−i3i30000i−ii−i00000000000000
χ452-2-22200-22-2-2200000-2222-22-22-2-2-2-20000222-22-2-22000000-22-22000000002-2002-2-220000000000000000000000
χ462-2-22200-22-2-2200000-2222-22-22-2-2-2-20000222-22-2-22000000-22-2200000000-2200-222-20000000000000000000000
χ472-2-22200-22-2-2200000-222-1-22-2-111-2-23−33−322-11-111-10000−331-11-13−33−3−33−332-200-111-100003−3−3300000000000000
χ482-2-22200-22-2-2200000-222-1-22-2-111-2-23−33−322-11-111-10000−331-11-13−33−3−33−33-22001-1-110000−333−300000000000000
χ492-2-22200-22-2-2200000-222-1-22-2-111-2-2−33−3322-11-111-100003−31-11-1−33−333−33−32-200-111-10000−333−300000000000000
χ502-2-22200-22-2-2200000-222-1-22-2-111-2-2−33−3322-11-111-100003−31-11-1−33−333−33−3-22001-1-1100003−3−3300000000000000
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
χ524444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-222-2-2-2-222111122-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ5344444-4-444444-4-4-4-4-444-2-2-2-2-2-2-2-2-2-22222-2-21111-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
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
χ5544-4-440000-44-4000000044-4-44-44-4000000004-4-4400000000000000000000000000000000000000000000000000
χ5644-4-440000-44-400000004-2-4-442-220023−23−232300-222-200000000000023−23−23230000000000000000000000000000000000
χ5744-4-440000-44-400000004-2-4-442-2200−232323−2300-222-2000000000000−232323−230000000000000000000000000000000000
χ5844-4-440000-44-40000000-2422-2-44-423−230000−2323-222-20000000023−23−232300000000000000000000000000000000000000
χ5944-4-440000-44-40000000-2422-2-44-4−2323000023−23-222-200000000−232323−2300000000000000000000000000000000000000
χ6044-4-440000-44-40000000-2-222-22-2223−2323−23−2323−23231-1-1100000000−333−3−333−33-3-33000000000000000000000000000000
χ6144-4-440000-44-40000000-2-222-22-2223−23−232323−23−23231-1-1100000000−333−33−3−33-333-3000000000000000000000000000000
χ6244-4-440000-44-40000000-2-222-22-22−232323−23−232323−231-1-11000000003−3−33−333−3-333-3000000000000000000000000000000
χ6344-4-440000-44-40000000-2-222-22-22−2323−232323−2323−231-1-11000000003−3−333−3−333-3-33000000000000000000000000000000
χ644-44-444-4004-4-404-400004-24-4-422-200-2-22200-2-222004-400000000-2-2220000000000000000000000000000000000
χ654-44-444-4004-4-404-40000-2-2-22222-223−23-2-22223−2311-1-100-2223−2300−3−33311-1-1−3−333000000000000000000000000000000
χ664-44-444-4004-4-404-40000-2-2-22222-2−2323-2-222−232311-1-100-22−23230033−3−311-1-133−3−3000000000000000000000000000000
χ674-44-44-44004-4-40-4400004-24-4-422-20022-2-200-2-22200-440000000022-2-20000000000000000000000000000000000
χ684-44-44-44004-4-40-440000-2-2-22222-223−2322-2-223−2311-1-1002-2−232300−3−333-1-11133−3−3000000000000000000000000000000
χ694-44-44-44004-4-40-440000-2-2-22222-2−232322-2-2−232311-1-1002-223−230033−3−3-1-111−3−333000000000000000000000000000000
χ704-4-444004-4-4-44000004-4-242-224-4-4-2-2000022-22-224-4000000-22-2200000000000000000000000000000000000000
χ714-4-444004-4-4-44000004-4-2-22-22-222-2-223−2323−23221-11-1-22000023−231-11-1−33−33−33−33000000000000000000000000000000
χ724-4-444004-4-4-44000004-4-2-22-22-222-2-2−2323−2323221-11-1-220000−23231-11-13−33−33−33−3000000000000000000000000000000
χ734-4-44400-44-4-4400000-44-242-224-4-4220000-2-2-22-22-440000002-22-200000000000000000000000000000000000000
χ744-4-44400-44-4-4400000-44-2-22-22-2222223−2323−23-2-21-11-12-20000−2323-11-11−33−333−33−3000000000000000000000000000000
χ754-4-44400-44-4-4400000-44-2-22-22-22222−2323−2323-2-21-11-12-2000023−23-11-113−33−3−33−33000000000000000000000000000000
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
χ786666-366-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3
χ796666-366-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3
χ806666-3-6-666-3-3-3-63333-3-300000000000000000000000000000000000000000000000000000000000000002-2-1-111
χ816666-3-6-666-3-3-3-63333-3-30000000000000000000000000000000000000000000000000000000000000000-2211-1-1
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
χ841212-12-12-600006-66000−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12-600006-660006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-612-1200-6660-6600000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-6-121200-66606-600000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-60012-1266-600000-660000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-600-121266-6000006-60000000000000000000000000000000000000000000000000000000000000000000000

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