Finite Group Databasebeta

← Group #13140041

Character table — Group #13140041

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222344446661212121226612123366666612121212366666666666121212121212121212121212121222446666888812121212242424242424242424661212
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
χ511111-1-1111111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-1111111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-1111111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ811111-1-1111111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-100000000000000
χ12222222222222222222222-12-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000111100000000000000
χ132222222-2-2222-2-2-2-2-2-2-2222222222222222-2-2-2-222-2-2-2-22-2-222-2-2-2-2-2-22222000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-2-2-2222-122-1-1-122222-1-2-211-1-11111-111-1-1-2-21111-1-1-1-100000000000000000000000000−i3i3−i3i3
χ152222222-2-2222-2-2-2-2-2-2-2222-122-1-1-122222-1-2-211-1-11111-111-1-1-2-21111-1-1-1-100000000000000000000000000i3−i3i3−i3
χ162222222-2-2222-2-2-2-2-2-2-222-12-1-1222-1-1-1-1-1-111-2-2-1-11111-1-2-222111111-1-1-1-10000−i3−i3i3i30000−i3−i3i3i300000000000000
χ172222222-2-2222-2-2-2-2-2-2-222-12-1-1222-1-1-1-1-1-111-2-2-1-11111-1-2-222111111-1-1-1-10000i3i3−i3−i30000i3i3−i3−i300000000000000
χ1822222-2-2222222222-2-2-2-2-22-122-1-1-12-2-2-2-2-1-2-211-1-11111-1-1-11122-1-1-1-111110000000000000000000000002-2-1-111
χ1922222-2-2222222222-2-2-2-2-22-122-1-1-12-2-2-2-2-1-2-211-1-11111-1-1-11122-1-1-1-11111000000000000000000000000-2211-1-1
χ2022222-2-2222222222-2-2-2-2-2-12-1-1222-11111-111-2-2-1-11111-122-2-2-1-1-1-1-1-1111122-2-2-1-1-1-10000111100000000000000
χ2122222-2-2222222222-2-2-2-2-2-12-1-1222-11111-111-2-2-1-11111-122-2-2-1-1-1-1-1-11111-2-22211110000-1-1-1-100000000000000
χ2222222-2-2-2-2222-2-2-2-2222-2-222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ2322222-2-2-2-2222-2-2-2-2222-2-22-122-1-1-12-2-2-2-2-122-1-1-1-1-1-1-1-1-11111-2-21111111100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-2222-2-22-122-1-1-12-2-2-2-2-122-1-1-1-1-1-1-1-1-11111-2-21111111100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-2222-2-2-12-1-1222-11111-1-1-122-1-1-1-1-1-1-1-2-2-2-211111111110000−i3−i3i3i30000i3i3−i3−i300000000000000
χ2622222-2-2-2-2222-2-2-2-2222-2-2-12-1-1222-11111-1-1-122-1-1-1-1-1-1-1-2-2-2-211111111110000i3i3−i3−i30000−i3−i3i3i300000000000000
χ2722-2-222i−2i002-2-200000002i−2i222-22-2-2-22i2i−2i−2i200002-20000-2002i−2i0000002i2i−2i−2i000000002−2−i2i2000022−2−2−i2−i2i2i2000000
χ2822-2-222i−2i002-2-200000002i−2i222-22-2-2-22i2i−2i−2i200002-20000-2002i−2i0000002i2i−2i−2i00000000−22i2−i20000−2−222i2i2−i2−i2000000
χ2922-2-22−2i2i002-2-20000000−2i2i222-22-2-2-2−2i−2i2i2i200002-20000-200−2i2i000000−2i−2i2i2i000000002−2i2−i2000022−2−2i2i2−i2−i2000000
χ3022-2-22−2i2i002-2-20000000−2i2i222-22-2-2-2−2i−2i2i2i200002-20000-200−2i2i000000−2i−2i2i2i00000000−22−i2i20000−2−222−i2−i2i2i2000000
χ312-2-222002-2-2-2222-2-20000022-2-2-22-22000020000-2-2000022-2002-222-2-20000002-2000000002-22-200000000000000
χ322-2-222002-2-2-2222-2-20000022-2-2-22-22000020000-2-2000022-2002-222-2-2000000-2200000000-22-2200000000000000
χ332-2-222002-2-2-2222-2-200000-1211-22-2-1−i3i3−i3i3-1−i3i30011−i3−i3i3i3-12-200-11-1-111−i3i3−i3i3002-2−i3i3−i3i30000-11-1100000000000000
χ342-2-222002-2-2-2222-2-200000-1211-22-2-1−i3i3−i3i3-1−i3i30011−i3−i3i3i3-12-200-11-1-111−i3i3−i3i300-22i3−i3i3−i300001-11-100000000000000
χ352-2-222002-2-2-2222-2-200000-1211-22-2-1i3−i3i3−i3-1i3−i30011i3i3−i3−i3-12-200-11-1-111i3−i3i3−i3002-2i3−i3i3−i30000-11-1100000000000000
χ362-2-222002-2-2-2222-2-200000-1211-22-2-1i3−i3i3−i3-1i3−i30011i3i3−i3−i3-12-200-11-1-111i3−i3i3−i300-22−i3i3−i3i300001-11-100000000000000
χ372-2-22200-22-2-22-2-2220000022-2-2-22-22000020000-2-200002-2200-22-2-22200002-2002-2-220000000000000000000000
χ382-2-22200-22-2-22-2-2220000022-2-2-22-22000020000-2-200002-2200-22-2-2220000-2200-222-20000000000000000000000
χ392-2-22200-22-2-22-2-22200000-1211-22-2-1−i3i3−i3i3-1i3−i30011i3i3−i3−i3-1-22001-111-1-1−i3i3−i3i32-200-111-10000−i3i3i3−i300000000000000
χ402-2-22200-22-2-22-2-22200000-1211-22-2-1−i3i3−i3i3-1i3−i30011i3i3−i3−i3-1-22001-111-1-1−i3i3−i3i3-22001-1-110000i3−i3−i3i300000000000000
χ412-2-22200-22-2-22-2-22200000-1211-22-2-1i3−i3i3−i3-1−i3i30011−i3−i3i3i3-1-22001-111-1-1i3−i3i3−i32-200-111-10000i3−i3−i3i300000000000000
χ422-2-22200-22-2-22-2-22200000-1211-22-2-1i3−i3i3−i3-1−i3i30011−i3−i3i3i3-1-22001-111-1-1i3−i3i3−i3-22001-1-110000−i3i3i3−i300000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-4444-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-222-1-1-1-11111000000000000000000000000000000
χ4544444-4-4444444444-4-4-4-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-21111-1-1-1-1000000000000000000000000000000
χ4644444-4-4-4-4444-4-4-4-4444-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4744-4-444i−4i004-4-400000004i−4i4-24-4-222-44i4i−4i−4i-20000-220000200−2i2i000000−2i−2i2i2i000000000000000000000000000000
χ4844-4-444i−4i004-4-400000004i−4i-24-224-4-42−2i−2i2i2i-20000-2200002004i−4i000000−2i−2i2i2i000000000000000000000000000000
χ4944-4-444i−4i004-4-400000004i−4i-2-2-22-2222−2i−2i2i2i100001-13-33-3-100−2i2i003i−3i3i−3iii−i−i000000000000000000000000000000
χ5044-4-444i−4i004-4-400000004i−4i-2-2-22-2222−2i−2i2i2i100001-1-33-33-100−2i2i00−3i3i−3i3iii−i−i000000000000000000000000000000
χ5144-4-44−4i4i004-4-40000000−4i4i4-24-4-222-4−4i−4i4i4i-20000-2200002002i−2i0000002i2i−2i−2i000000000000000000000000000000
χ5244-4-44−4i4i004-4-40000000−4i4i-24-224-4-422i2i−2i−2i-20000-220000200−4i4i0000002i2i−2i−2i000000000000000000000000000000
χ5344-4-44−4i4i004-4-40000000−4i4i-2-2-22-22222i2i−2i−2i100001-13-33-3-1002i−2i00−3i3i−3i3i−i−iii000000000000000000000000000000
χ5444-4-44−4i4i004-4-40000000−4i4i-2-2-22-22222i2i−2i−2i100001-1-33-33-1002i−2i003i−3i3i−3i−i−iii000000000000000000000000000000
χ554-44-440000-44-400000000044-44-4-44-4000040000-440000-400000000000000000000000000000000000000000000
χ564-44-440000-44-40000000004-2-4422-2-40000-200−2i32i32-2−2i32i32i3−2i3200000000000000000000000000000000000000000000
χ574-44-440000-44-40000000004-2-4422-2-40000-2002i3−2i32-22i3−2i3−2i32i3200000000000000000000000000000000000000000000
χ584-44-440000-44-4000000000-242-2-4-44223−23−2323-200002-200002000000000023−23−2323000000000000000000000000000000
χ594-44-440000-44-4000000000-242-2-4-442−232323−23-200002-2000020000000000−232323−23000000000000000000000000000000
χ604-44-440000-44-4000000000-2-22-222-2223−23−2323100−2i32i3-11i3−i3−i3i3-1000000−3i3i3i−3i−333−3000000000000000000000000000000
χ614-44-440000-44-4000000000-2-22-222-2223−23−23231002i3−2i3-11−i3i3i3−i3-10000003i−3i−3i3i−333−3000000000000000000000000000000
χ624-44-440000-44-4000000000-2-22-222-22−232323−23100−2i32i3-11i3−i3−i3i3-10000003i−3i−3i3i3−3−33000000000000000000000000000000
χ634-44-440000-44-4000000000-2-22-222-22−232323−231002i3−2i3-11−i3i3i3−i3-1000000−3i3i3i−3i3−3−33000000000000000000000000000000
χ644-4-444004-4-4-4444-4-4000004-2-4-42-2240000-20000220000-2-22004-4-2-2220000000000000000000000000000000000
χ654-4-444004-4-4-4444-4-400000-2-2222-22-2−2i32i3−2i32i31−2i32i300-1-1i3i3−i3−i31-2200-2211-1-1i3−i3i3−i3000000000000000000000000000000
χ664-4-444004-4-4-4444-4-400000-2-2222-22-22i3−2i32i3−2i312i3−2i300-1-1−i3−i3i3i31-2200-2211-1-1−i3i3−i3i3000000000000000000000000000000
χ674-4-44400-44-4-44-4-444000004-2-4-42-2240000-20000220000-22-200-4422-2-20000000000000000000000000000000000
χ684-4-44400-44-4-44-4-44400000-2-2222-22-2−2i32i3−2i32i312i3−2i300-1-1−i3−i3i3i312-2002-2-1-111i3−i3i3−i3000000000000000000000000000000
χ694-4-44400-44-4-44-4-44400000-2-2222-22-22i3−2i32i3−2i31−2i32i300-1-1i3i3−i3−i312-2002-2-1-111−i3i3−i3i3000000000000000000000000000000
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
χ726666-366-6-6-3-3-33333-633-3-30000000000000000000000000000000000000000000000000000003−33−33−33−3000000
χ736666-366-6-6-3-3-33333-633-3-3000000000000000000000000000000000000000000000000000000−33−33−33−33000000
χ746666-3-6-666-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000000022-2-20000-1-1-1-11111000000
χ756666-3-6-666-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000-2-22200001111-1-1-1-1000000
χ766666-3-6-6-6-6-3-3-333336-3-3330000000000000000000000000000000000000000000000000000003−33−3−33−33000000
χ776666-3-6-6-6-6-3-3-333336-3-333000000000000000000000000000000000000000000000000000000−33−333−33−3000000
χ7866-6-6-36i−6i00-33333−3333−330−3i33i3−3i3i00000000000000000000000000000000000000000000002−2−i2i20000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ7966-6-6-36i−6i00-33333−3333−330−3i33i3−3i3i0000000000000000000000000000000000000000000000−22i2−i20000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ8066-6-6-36i−6i00-333−3333−333303i3−3i3−3i3i00000000000000000000000000000000000000000000002−2−i2i20000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ8166-6-6-36i−6i00-333−3333−333303i3−3i3−3i3i0000000000000000000000000000000000000000000000−22i2−i20000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ8266-6-6-3−6i6i00-33333−3333−3303i3−3i33i−3i00000000000000000000000000000000000000000000002−2i2−i20000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ8366-6-6-3−6i6i00-33333−3333−3303i3−3i33i−3i0000000000000000000000000000000000000000000000−22−i2i20000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ8466-6-6-3−6i6i00-333−3333−33330−3i33i33i−3i00000000000000000000000000000000000000000000002−2i2−i20000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ8566-6-6-3−6i6i00-333−3333−33330−3i33i33i−3i0000000000000000000000000000000000000000000000−22−i2i20000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ8612-1212-12-600006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-600006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-60012-1266-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-600-121266-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000

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