Finite Group Databasebeta

← Group #13137427

Character table — Group #13137427

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122234444666412121212121233666666121212121212121236661212121212121212121212121212121212121212444488881212121212121212242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ511111-1-111111-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ922222222222222222222-1222-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ1022222222222222222222-1222-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ112222222222222222222-12-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ122222222222222222222-12-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-2222-222-2-2-2-222222222-2-22222-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-222-2-2-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-122-2-211111111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ152222222-2-2222-222-2-2-2-22-1222-1-1-1-2-2-1-1-1-1-2-2-1-1-1-122-2-211111111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ162222222-2-2222-222-2-2-2-2-12-1-1-122211222211-1-1-1-1-1-111-2-2-2-21111-1-1-1-11111000000000000000033−3−333−3−3000000
χ172222222-2-2222-222-2-2-2-2-12-1-1-122211222211-1-1-1-1-1-111-2-2-2-21111-1-1-1-111110000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-2-2-2222-1222-1-1-122111122-1-1-1-1-2-2-2-2-1-111-1-1-1-11111111122-2-20000-1-1-1-1111100000000000000
χ1922222-2-222222-2-2-2-2-2222-1222-1-1-122111122-1-1-1-1-2-2-2-2-1-111-1-1-1-111111111-2-22200001111-1-1-1-100000000000000
χ2022222-2-222222-2-2-2-2-222-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1111122-2-2-1-1-1-111111111000022-2-200000000-1-1-1-11111000000
χ2122222-2-222222-2-2-2-2-222-12-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1111122-2-2-1-1-1-1111111110000-2-222000000001111-1-1-1-1000000
χ2222222-2-2-2-22222-2-222-2-222222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222-2-2-2-22222-2-222-2-22-1222-1-1-1-2-21111-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ2422222-2-2-2-22222-2-222-2-22-1222-1-1-1-2-21111-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ2522222-2-2-2-22222-2-222-2-2-12-1-1-122211-2-2-2-211-1-1-1-111-1-1-2-22211111111-1-1-1-1000000000000000033−3−3−3−333000000
χ2622222-2-2-2-22222-2-222-2-2-12-1-1-122211-2-2-2-211-1-1-1-111-1-1-2-22211111111-1-1-1-10000000000000000−3−33333−3−3000000
χ272-22-222i−2i002-2-202i−2i0000222-2-2-22-2002i2i−2i−2i0022-2-22i−2i00000000002i2i−2i−2i000000002−2−i2i2000000002−22−2−i2i2−i2i2000000
χ282-22-222i−2i002-2-202i−2i0000222-2-2-22-2002i2i−2i−2i0022-2-22i−2i00000000002i2i−2i−2i00000000−22i2−i200000000−22−22i2−i2i2−i2000000
χ292-22-222i−2i002-2-202i−2i0000-12-111-22-23−32i2i−2i−2i3−3-1-111−ii−i3i3000033−3−3−i−iii−i3−i3i3i300002−2−i2i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ302-22-222i−2i002-2-202i−2i0000-12-111-22-23−32i2i−2i−2i3−3-1-111−ii−i3i3000033−3−3−i−iii−i3−i3i3i30000−22i2−i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ312-22-222i−2i002-2-202i−2i0000-12-111-22-2−332i2i−2i−2i−33-1-111−iii3−i30000−3−333−i−iiii3i3−i3−i300002−2−i2i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ322-22-222i−2i002-2-202i−2i0000-12-111-22-2−332i2i−2i−2i−33-1-111−iii3−i30000−3−333−i−iiii3i3−i3−i30000−22i2−i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ332-22-22−2i2i002-2-20−2i2i0000222-2-2-22-200−2i−2i2i2i0022-2-2−2i2i0000000000−2i−2i2i2i000000002−2i2−i2000000002−22−2i2−i2i2−i2000000
χ342-22-22−2i2i002-2-20−2i2i0000222-2-2-22-200−2i−2i2i2i0022-2-2−2i2i0000000000−2i−2i2i2i00000000−22−i2i200000000−22−22−i2i2−i2i2000000
χ352-22-22−2i2i002-2-20−2i2i0000-12-111-22-23−3−2i−2i2i2i3−3-1-111i−ii3−i3000033−3−3ii−i−ii3i3−i3−i300002−2i2−i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ362-22-22−2i2i002-2-20−2i2i0000-12-111-22-23−3−2i−2i2i2i3−3-1-111i−ii3−i3000033−3−3ii−i−ii3i3−i3−i30000−22−i2i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ372-22-22−2i2i002-2-20−2i2i0000-12-111-22-2−33−2i−2i2i2i−33-1-111i−i−i3i30000−3−333ii−i−i−i3−i3i3i300002−2i2−i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ382-22-22−2i2i002-2-20−2i2i0000-12-111-22-2−33−2i−2i2i2i−33-1-111i−i−i3i30000−3−333ii−i−i−i3−i3i3i30000−22−i2i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ392-2-222002-2-2-22000002-222-22-2-2-22220000-2-22-22-200002-2002-22-2000000002i−2i0000002i−2i2i−2i000000000000000000
χ402-2-222002-2-2-22000002-222-22-2-2-22220000-2-22-22-200002-2002-22-200000000−2i2i000000−2i2i−2i2i000000000000000000
χ412-2-222002-2-2-22000002-22-1-22-211-1223−33−3-2-2-11-110000-113−3-11-113−33−33−33−32i−2i000000−ii−ii−i3i3−i3i300000000000000
χ422-2-222002-2-2-22000002-22-1-22-211-1223−33−3-2-2-11-110000-113−3-11-113−33−33−33−3−2i2i000000i−ii−ii3−i3i3−i300000000000000
χ432-2-222002-2-2-22000002-22-1-22-211-122−33−33-2-2-11-110000-11−33-11-11−33−33−33−332i−2i000000−ii−iii3−i3i3−i300000000000000
χ442-2-222002-2-2-22000002-22-1-22-211-122−33−33-2-2-11-110000-11−33-11-11−33−33−33−33−2i2i000000i−ii−i−i3i3−i3i300000000000000
χ452-2-22200-22-2-2200000-2222-22-2-2-22-2-20000222-22-20000-2200-22-2200000000002-2000000002-2-2200000000000000
χ462-2-22200-22-2-2200000-2222-22-2-2-22-2-20000222-22-20000-2200-22-220000000000-2200000000-222-200000000000000
χ472-2-22200-22-2-2200000-222-1-22-211-1-2-23−33−322-11-1100001-1−331-11-13−33−3−33−33002-200003−3−33-111-100000000000000
χ482-2-22200-22-2-2200000-222-1-22-211-1-2-23−33−322-11-1100001-1−331-11-13−33−3−33−3300-220000−333−31-1-1100000000000000
χ492-2-22200-22-2-2200000-222-1-22-211-1-2-2−33−3322-11-1100001-13−31-11-1−33−333−33−3002-20000−333−3-111-100000000000000
χ502-2-22200-22-2-2200000-222-1-22-211-1-2-2−33−3322-11-1100001-13−31-11-1−33−333−33−300-2200003−3−331-1-1100000000000000
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
χ524444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-222-2-2-2-2221111-2-2222222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ5344444-4-444444-4-4-4-4-444-2-2-2-2-2-2-2-2-2-22222-2-211112222-2-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5444444-4-4-4-44444-4-444-4-4-2-2-2-2-2-2-2-222222222111122-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ5544-4-440000-44-4000000044-4-444-4-4000000004-4-4400000000000000000000000000000000000000000000000000
χ5644-4-440000-44-400000004-2-4-44-22200−2i32i32i3−2i300-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ5744-4-440000-44-400000004-2-4-44-222002i3−2i3−2i32i300-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ5844-4-440000-44-40000000-2422-24-4-423−230000−2323-222-20000000023−23−232300000000000000000000000000000000000000
χ5944-4-440000-44-40000000-2422-24-4-4−2323000023−23-222-200000000−232323−2300000000000000000000000000000000000000
χ6044-4-440000-44-40000000-2-222-2-22223−23−2i32i32i3−2i3−23231-1-1100000000−333−3i3−i3−i3i33i−3i−3i3i000000000000000000000000000000
χ6144-4-440000-44-40000000-2-222-2-22223−232i3−2i3−2i32i3−23231-1-1100000000−333−3−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000
χ6244-4-440000-44-40000000-2-222-2-222−2323−2i32i32i3−2i323−231-1-11000000003−3−33i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000
χ6344-4-440000-44-40000000-2-222-2-222−23232i3−2i3−2i32i323−231-1-11000000003−3−33−i3i3i3−i33i−3i−3i3i000000000000000000000000000000
χ644-44-444i−4i004-4-404i−4i00004-24-4-42-2200−2i−2i2i2i00-2-2224i−4i0000000000−2i−2i2i2i0000000000000000000000000000000000
χ654-44-444i−4i004-4-404i−4i0000-2-2-2222-2223−23−2i−2i2i2i23−2311-1-1−2i2i−2i32i30000−3−333ii−i−ii3i3−i3−i3000000000000000000000000000000
χ664-44-444i−4i004-4-404i−4i0000-2-2-2222-22−2323−2i−2i2i2i−232311-1-1−2i2i2i3−2i3000033−3−3ii−i−i−i3−i3i3i3000000000000000000000000000000
χ674-44-44−4i4i004-4-40−4i4i00004-24-4-42-22002i2i−2i−2i00-2-222−4i4i00000000002i2i−2i−2i0000000000000000000000000000000000
χ684-44-44−4i4i004-4-40−4i4i0000-2-2-2222-2223−232i2i−2i−2i23−2311-1-12i−2i2i3−2i30000−3−333−i−iii−i3−i3i3i3000000000000000000000000000000
χ694-44-44−4i4i004-4-40−4i4i0000-2-2-2222-22−23232i2i−2i−2i−232311-1-12i−2i−2i32i3000033−3−3−i−iiii3i3−i3−i3000000000000000000000000000000
χ704-4-444004-4-4-44000004-4-242-22-4-44-2-2000022-22-2200004-400-22-2200000000000000000000000000000000000000
χ714-4-444004-4-4-44000004-4-2-22-2222-2-2-223−2323−23221-11-10000-2223−231-11-1−33−33−33−33000000000000000000000000000000
χ724-4-444004-4-4-44000004-4-2-22-2222-2-2-2−2323−2323221-11-10000-22−23231-11-13−33−33−33−3000000000000000000000000000000
χ734-4-44400-44-4-4400000-44-242-22-4-44220000-2-2-22-220000-44002-22-200000000000000000000000000000000000000
χ744-4-44400-44-4-4400000-44-2-22-2222-22223−2323−23-2-21-11-100002-2−2323-11-11−33−333−33−3000000000000000000000000000000
χ754-4-44400-44-4-4400000-44-2-22-2222-222−2323−2323-2-21-11-100002-223−23-11-113−33−3−33−33000000000000000000000000000000
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
χ841212-12-12-600006-6600063−63000000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12-600006-66000−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-612i−12i00-6660−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-6−12i12i00-66606i−6i00000000000000000000000000000000000000000000000000000000000000000000000000
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.