Finite Group Databasebeta

← Group #13137385

Character table — Group #13137385

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122234444666121212124121212123366666612121212366612121212121212121212121212121212121212121212444488881212121212121212242424242424242424661212
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
χ511111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-1111111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-122-1-12-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ12222222222222222222222-12-122-1-12-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ132222222-2-2222-2-2-2-2-222-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-222-2-22-12-1-122-12222-1-1-1-1-1-111-2-211-2-21111-1-1-1-1111100000000000000000000000000−i3i3−i3i3
χ152222222-2-2222-2-2-2-2-222-2-22-12-1-122-12222-1-1-1-1-1-111-2-211-2-21111-1-1-1-1111100000000000000000000000000i3−i3i3−i3
χ162222222-2-2222-2-2-2-2-222-2-2-12-122-1-12-1-1-1-1-1-1-1-122-2-211-2-2111111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ172222222-2-2222-2-2-2-2-222-2-2-12-122-1-12-1-1-1-1-1-1-1-122-2-211-2-2111111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ1822222-2-2222222222-2-2-2-2-22-12-1-122-1-2-2-2-2-1-1-1-1111122-1-1-2-2-1-1-1-1111111110000000000000000000000002-2-1-111
χ1922222-2-2222222222-2-2-2-2-22-12-1-122-1-2-2-2-2-1-1-1-1111122-1-1-2-2-1-1-1-111111111000000000000000000000000-2211-1-1
χ2022222-2-2222222222-2-2-2-2-2-12-122-1-121111-1-1-1-1-2-2-2-2-1-12211-1-1-1-11111111122-2-20000-1-1-1-1111100000000000000
χ2122222-2-2222222222-2-2-2-2-2-12-122-1-121111-1-1-1-1-2-2-2-2-1-12211-1-1-1-111111111-2-22200001111-1-1-1-100000000000000
χ2222222-2-2-2-2222-2-2-2-22-2-22222222222-2-2-2-22222-2-222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222-2-2-2-2222-2-2-2-22-2-2222-12-1-122-1-2-2-2-2-1-1-1-111-1-1-2-2112211111111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-22-2-2222-12-1-122-1-2-2-2-2-1-1-1-111-1-1-2-2112211111111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-22-2-222-12-122-1-121111-1-1-1-1-2-22211-2-2-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ2622222-2-2-2-2222-2-2-2-22-2-222-12-122-1-121111-1-1-1-1-2-22211-2-2-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ272-22-222i−2i002-2-2000002i−2i0022-22-22-2-22i2i−2i−2i22-2-22i−2i0000000000002i2i−2i−2i000000002−2−i2i20000000022−2−2−i2−i2i2i2000000
χ282-22-222i−2i002-2-2000002i−2i0022-22-22-2-22i2i−2i−2i22-2-22i−2i0000000000002i2i−2i−2i00000000−22i2−i200000000−2−222i2i2−i2−i2000000
χ292-22-22−2i2i002-2-200000−2i2i0022-22-22-2-2−2i−2i2i2i22-2-2−2i2i000000000000−2i−2i2i2i000000002−2i2−i20000000022−2−2i2i2−i2−i2000000
χ302-22-22−2i2i002-2-200000−2i2i0022-22-22-2-2−2i−2i2i2i22-2-2−2i2i000000000000−2i−2i2i2i00000000−22−i2i200000000−2−222−i2−i2i2i2000000
χ312-2-222002-2-22-222-2-20000022-2-2-2-22200002-22-200002-22-20022-2-2000000002i−2i0000002i−2i2i−2i000000000000000000
χ322-2-222002-2-22-222-2-20000022-2-2-2-22200002-22-200002-22-20022-2-200000000−2i2i000000−2i2i−2i2i000000000000000000
χ332-2-222002-2-22-222-2-200000-121-2-21-123−33−3-11-110000-112-23−3-1-1113−33−333−3−32i−2i000000−ii−ii−i3i3−i3i300000000000000
χ342-2-222002-2-22-222-2-200000-121-2-21-123−33−3-11-110000-112-23−3-1-1113−33−333−3−3−2i2i000000i−ii−ii3−i3i3−i300000000000000
χ352-2-222002-2-22-222-2-200000-121-2-21-12−33−33-11-110000-112-2−33-1-111−33−33−3−3332i−2i000000−ii−iii3−i3i3−i300000000000000
χ362-2-222002-2-22-222-2-200000-121-2-21-12−33−33-11-110000-112-2−33-1-111−33−33−3−333−2i2i000000i−ii−i−i3i3−i3i300000000000000
χ372-2-22200-22-22-2-2-2220000022-2-2-2-22200002-22-20000-22-2200-2-22200000000002-2000000002-2-2200000000000000
χ382-2-22200-22-22-2-2-2220000022-2-2-2-22200002-22-20000-22-2200-2-2220000000000-2200000000-222-200000000000000
χ392-2-22200-22-22-2-2-22200000-121-2-21-123−33−3-11-1100001-1-22−3311-1-13−33−3−3−333002-200003−3−33-111-100000000000000
χ402-2-22200-22-22-2-2-22200000-121-2-21-123−33−3-11-1100001-1-22−3311-1-13−33−3−3−33300-220000−333−31-1-1100000000000000
χ412-2-22200-22-22-2-2-22200000-121-2-21-12−33−33-11-1100001-1-223−311-1-1−33−3333−3−3002-20000−333−3-111-100000000000000
χ422-2-22200-22-22-2-2-22200000-121-2-21-12−33−33-11-1100001-1-223−311-1-1−33−3333−3−300-2200003−3−331-1-1100000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ444444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-2-222222222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4544444-4-4444444444-4-4-4-4-4-2-2-2-2-2-2-2-2222211112222-2-2-2-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4644444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-22222111122-2-22222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4744-4-440000-4-44000000000444-44-4-4-400004-4-440000000000000000000000000000000000000000000000000000
χ4844-4-440000-4-440000000004-242-2-4-420000-222-20023−230000000000000023−2323−23000000000000000000000000000000
χ4944-4-440000-4-440000000004-242-2-4-420000-222-200−232300000000000000−2323−2323000000000000000000000000000000
χ5044-4-440000-4-44000000000-24-2-4422-4−2i32i32i3−2i3-222-200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ5144-4-440000-4-44000000000-24-2-4422-42i3−2i3−2i32i3-222-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ5244-4-440000-4-44000000000-2-2-22-2222−2i32i32i3−2i31-1-110023−230000003i−3i3i−3ii3−i3−i3i3−33−33000000000000000000000000000000
χ5344-4-440000-4-44000000000-2-2-22-2222−2i32i32i3−2i31-1-1100−2323000000−3i3i−3i3ii3−i3−i3i33−33−3000000000000000000000000000000
χ5444-4-440000-4-44000000000-2-2-22-22222i3−2i3−2i32i31-1-110023−23000000−3i3i−3i3i−i3i3i3−i3−33−33000000000000000000000000000000
χ5544-4-440000-4-44000000000-2-2-22-22222i3−2i3−2i32i31-1-1100−23230000003i−3i3i−3i−i3i3i3−i33−33−3000000000000000000000000000000
χ564-44-444i−4i004-4-4000004i−4i004-2-4-224-424i4i−4i−4i-2-222−2i2i000000000000−2i−2i2i2i0000000000000000000000000000000000
χ574-44-444i−4i004-4-4000004i−4i00-2424-4-22-4−2i−2i2i2i-2-2224i−4i000000000000−2i−2i2i2i0000000000000000000000000000000000
χ584-44-444i−4i004-4-4000004i−4i00-2-22-22-222−2i−2i2i2i11-1-1−2i2i000000003i−3i−3i3iii−i−i3-3-33000000000000000000000000000000
χ594-44-444i−4i004-4-4000004i−4i00-2-22-22-222−2i−2i2i2i11-1-1−2i2i00000000−3i3i3i−3iii−i−i-333-3000000000000000000000000000000
χ604-44-44−4i4i004-4-400000−4i4i004-2-4-224-42−4i−4i4i4i-2-2222i−2i0000000000002i2i−2i−2i0000000000000000000000000000000000
χ614-44-44−4i4i004-4-400000−4i4i00-2424-4-22-42i2i−2i−2i-2-222−4i4i0000000000002i2i−2i−2i0000000000000000000000000000000000
χ624-44-44−4i4i004-4-400000−4i4i00-2-22-22-2222i2i−2i−2i11-1-12i−2i000000003i−3i−3i3i−i−iii-333-3000000000000000000000000000000
χ634-44-44−4i4i004-4-400000−4i4i00-2-22-22-2222i2i−2i−2i11-1-12i−2i00000000−3i3i3i−3i−i−iii3-3-33000000000000000000000000000000
χ644-4-444004-4-44-444-4-4000004-2-422-44-20000-22-2200004-4-2200-2-22200000000000000000000000000000000000000
χ654-4-444004-4-44-444-4-400000-2-22222-2-223−2323−231-11-10000-22-2223−2311-1-1−33−33−3−333000000000000000000000000000000
χ664-4-444004-4-44-444-4-400000-2-22222-2-2−2323−23231-11-10000-22-22−232311-1-13−33−333−3−3000000000000000000000000000000
χ674-4-44400-44-44-4-4-444000004-2-422-44-20000-22-220000-442-20022-2-200000000000000000000000000000000000000
χ684-4-44400-44-44-4-4-44400000-2-22222-2-223−2323−231-11-100002-22-2−2323-1-111−33−3333−3−3000000000000000000000000000000
χ694-4-44400-44-44-4-4-44400000-2-22222-2-2−2323−23231-11-100002-22-223−23-1-1113−33−3−3−333000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-1000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-20000000011111111000000
χ726666-366-6-6-3-3-33333-6-3-3330000000000000000000000000000000000000000000000000000003−33−33−33−3000000
χ736666-366-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000000000000000−33−33−33−33000000
χ746666-3-6-666-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-200000000-1-1-1-11111000000
χ756666-3-6-666-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222000000001111-1-1-1-1000000
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
χ786-66-6-36i−6i00-33333−3333−330−3i3i−3i33i30000000000000000000000000000000000000000002−2−i2i200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ796-66-6-36i−6i00-33333−3333−330−3i3i−3i33i3000000000000000000000000000000000000000000−22i2−i200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ806-66-6-36i−6i00-333−3333−33330−3i3i3i3−3i30000000000000000000000000000000000000000002−2−i2i200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ816-66-6-36i−6i00-333−3333−33330−3i3i3i3−3i3000000000000000000000000000000000000000000−22i2−i200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ826-66-6-3−6i6i00-33333−3333−3303i−3i3i3−3i30000000000000000000000000000000000000000002−2i2−i200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ836-66-6-3−6i6i00-33333−3333−3303i−3i3i3−3i3000000000000000000000000000000000000000000−22−i2i200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ846-66-6-3−6i6i00-333−3333−333303i−3i−3i33i30000000000000000000000000000000000000000002−2i2−i200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ856-66-6-3−6i6i00-333−3333−333303i−3i−3i33i3000000000000000000000000000000000000000000−22−i2i200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ861212-12-12-6000066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-6000066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-60012-126-66-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-600-12126-6666-6-60000000000000000000000000000000000000000000000000000000000000000000000000

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