Finite Group Databasebeta

← Group #13140194

Character table — Group #13140194

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
χ511111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-2000011111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-22-2-2-2-222-2-2-2-22-2-22222-2-2-2-22222000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-12-1221111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-1000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-12-1221111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-10000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-111110000000000000000000000002-2-1-111
χ1922222-2-222222-2-2-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-11111000000000000000000000000-2211-1-1
χ2022222-2-222222-2-2-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-111110000000022-2-20000-1-1-1-11111000000
χ2122222-2-222222-2-2-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-1111100000000-2-22200001111-1-1-1-1000000
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
χ2322222-2-2-2-2222-2-2-2-2222-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-2222-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-2222-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−3−3−333000000
χ2622222-2-2-2-2222-2-2-2-2222-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−33333−3−3000000
χ2722-2-222i−2i002-2-22i2i−2i−2i00000222-22-2-2-20000200002-20000-2002i−2i2i−2i00002i2i−2i−2i000000002−2−i2i200002−22−2−i2i2−i2i2000000
χ2822-2-222i−2i002-2-22i2i−2i−2i00000222-22-2-2-20000200002-20000-2002i−2i2i−2i00002i2i−2i−2i00000000−22i2−i20000−22−22i2−i2i2−i2000000
χ2922-2-222i−2i002-2-22i2i−2i−2i00000-12-1121-2-233−3−3-1−i3i300-11−i3−i3i3i3100−ii2i−2i33−3−3−i−iii000000002−2−i2i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ3022-2-222i−2i002-2-22i2i−2i−2i00000-12-1121-2-233−3−3-1−i3i300-11−i3−i3i3i3100−ii2i−2i33−3−3−i−iii00000000−22i2−i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ3122-2-222i−2i002-2-22i2i−2i−2i00000-12-1121-2-2−3−333-1i3−i300-11i3i3−i3−i3100−ii2i−2i−3−333−i−iii000000002−2−i2i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ3222-2-222i−2i002-2-22i2i−2i−2i00000-12-1121-2-2−3−333-1i3−i300-11i3i3−i3−i3100−ii2i−2i−3−333−i−iii00000000−22i2−i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ3322-2-22−2i2i002-2-2−2i−2i2i2i00000222-22-2-2-20000200002-20000-200−2i2i−2i2i0000−2i−2i2i2i000000002−2i2−i200002−22−2i2−i2i2−i2000000
χ3422-2-22−2i2i002-2-2−2i−2i2i2i00000222-22-2-2-20000200002-20000-200−2i2i−2i2i0000−2i−2i2i2i00000000−22−i2i20000−22−22−i2i2−i2i2000000
χ3522-2-22−2i2i002-2-2−2i−2i2i2i00000-12-1121-2-233−3−3-1i3−i300-11i3i3−i3−i3100i−i−2i2i33−3−3ii−i−i000000002−2i2−i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ3622-2-22−2i2i002-2-2−2i−2i2i2i00000-12-1121-2-233−3−3-1i3−i300-11i3i3−i3−i3100i−i−2i2i33−3−3ii−i−i00000000−22−i2i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ3722-2-22−2i2i002-2-2−2i−2i2i2i00000-12-1121-2-2−3−333-1−i3i300-11−i3−i3i3i3100i−i−2i2i−3−333ii−i−i000000002−2i2−i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ3822-2-22−2i2i002-2-2−2i−2i2i2i00000-12-1121-2-2−3−333-1−i3i300-11−i3−i3i3i3100i−i−2i2i−3−333ii−i−i00000000−22−i2i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ392-2-222002-2-2-2200000002-222-2-2-222-22-22-220000-2-2000022-200002-22-20000002-20000000022-2-200000000000000
χ402-2-222002-2-2-2200000002-222-2-2-222-22-22-220000-2-2000022-200002-22-2000000-2200000000-2-22200000000000000
χ412-2-22200-22-2-220000000-2222-2-2-222-2-22-2220000-2-200002-220000-22-2200002-20022-2-20000000000000000000000
χ422-2-22200-22-2-220000000-2222-2-2-222-2-22-2220000-2-200002-220000-22-220000-2200-2-2220000000000000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ4544444-4-444444-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000
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−4i004-4-44i4i−4i−4i000004-24-4-2-4220000-20000-2200002004i−4i−2i2i0000−2i−2i2i2i000000000000000000000000000000
χ4844-4-444i−4i004-4-44i4i−4i−4i00000-2-2-22-22222323−23−231−2i32i3001-1i3i3−i3−i3-100−2i2i−2i2i−3−333ii−i−i000000000000000000000000000000
χ4944-4-444i−4i004-4-44i4i−4i−4i00000-2-2-22-2222−23−23232312i3−2i3001-1−i3−i3i3i3-100−2i2i−2i2i33−3−3ii−i−i000000000000000000000000000000
χ5044-4-44−4i4i004-4-4−4i−4i4i4i000004-24-4-2-4220000-20000-220000200−4i4i2i−2i00002i2i−2i−2i000000000000000000000000000000
χ5144-4-44−4i4i004-4-4−4i−4i4i4i00000-2-2-22-22222323−23−2312i3−2i3001-1−i3−i3i3i3-1002i−2i2i−2i−3−333−i−iii000000000000000000000000000000
χ5244-4-44−4i4i004-4-4−4i−4i4i4i00000-2-2-22-2222−23−2323231−2i32i3001-1i3i3−i3−i3-1002i−2i2i−2i33−3−3−i−iii000000000000000000000000000000
χ534-44-440000-44-400000000044-44-4-4-44000040000-440000-400000000000000000000000000000000000000000000
χ544-44-440000-44-40000000004-2-442-42-20000-200−2i32i32-2−2i32i3−2i32i3200000000000000000000000000000000000000000000
χ554-44-440000-44-40000000004-2-442-42-20000-2002i3−2i32-22i3−2i32i3−2i3200000000000000000000000000000000000000000000
χ564-44-440000-44-4000000000-242-2-42-4423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ574-44-440000-44-4000000000-242-2-42-44−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ584-44-440000-44-4000000000-2-22-2222-223−23−2323100−2i32i3-11i3−i3i3−i3-1000000−333−33i−3i3i−3i000000000000000000000000000000
χ594-44-440000-44-4000000000-2-22-2222-223−23−23231002i3−2i3-11−i3i3−i3i3-1000000−333−3−3i3i−3i3i000000000000000000000000000000
χ604-44-440000-44-4000000000-2-22-2222-2−232323−23100−2i32i3-11i3−i3i3−i3-10000003−3−33−3i3i−3i3i000000000000000000000000000000
χ614-44-440000-44-4000000000-2-22-2222-2−232323−231002i3−2i3-11−i3i3−i3i3-10000003−3−333i−3i3i−3i000000000000000000000000000000
χ624-4-444004-4-4-4400000004-44-2-4-424-224-44-4-20000220000-2-220000-22-220000000000000000000000000000000000
χ634-4-444004-4-4-4400000004-4-2422-4-24-4-22-22-20000220000-24-40000-22-220000000000000000000000000000000000
χ644-4-444004-4-4-4400000004-4-2-2222-2-22-22-2210000-1-13-3-331-2200001-11-1-333-3000000000000000000000000000000
χ654-4-444004-4-4-4400000004-4-2-2222-2-22-22-2210000-1-1-333-31-2200001-11-13-3-33000000000000000000000000000000
χ664-4-44400-44-4-440000000-444-2-4-424-22-44-44-20000220000-22-200002-22-20000000000000000000000000000000000
χ674-4-44400-44-4-440000000-44-2422-4-24-42-22-2-20000220000-2-4400002-22-20000000000000000000000000000000000
χ684-4-44400-44-4-440000000-44-2-2222-2-222-22-210000-1-13-3-3312-20000-11-113-3-33000000000000000000000000000000
χ694-4-44400-44-4-440000000-44-2-2222-2-222-22-210000-1-1-333-312-20000-11-11-333-3000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002222-1-1-1-10000-1-1-1-100000000000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-211110000111100000000000000
χ726666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000−i3i3−i3i30000−i3i3−i3i300000000000000
χ736666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000i3−i3i3−i30000i3−i3i3−i300000000000000
χ746666-3-6-666-3-3-33333-633-3-30000000000000000000000000000000000000022-2-2-1-1-1-10000111100000000000000
χ756666-3-6-666-3-3-33333-633-3-300000000000000000000000000000000000000-2-22211110000-1-1-1-100000000000000
χ766666-3-6-6-6-6-3-3-333336-3-333000000000000000000000000000000000000000000−i3i3−i3i30000i3−i3i3−i300000000000000
χ776666-3-6-6-6-6-3-3-333336-3-333000000000000000000000000000000000000000000i3−i3i3−i30000−i3i3−i3i300000000000000
χ786-6-66-3006-633-3−3i33i3−3i33i30−3i33i3-3300000000000000000000000000000000000000002-2−i3i3i3−i30000-1-11100000000000000
χ796-6-66-3006-633-3−3i33i3−3i33i30−3i33i3-330000000000000000000000000000000000000000-22i3−i3−i3i3000011-1-100000000000000
χ806-6-66-3006-633-33i3−3i33i3−3i303i3−3i3-3300000000000000000000000000000000000000002-2i3−i3−i3i30000-1-11100000000000000
χ816-6-66-3006-633-33i3−3i33i3−3i303i3−3i3-330000000000000000000000000000000000000000-22−i3i3i3−i3000011-1-100000000000000
χ826-6-66-300-6633-3−3i33i3−3i33i303i3−3i33-3000000000000000000000000000000000000002-200-1-1110000−i3i3i3−i300000000000000
χ836-6-66-300-6633-3−3i33i3−3i33i303i3−3i33-300000000000000000000000000000000000000-220011-1-10000i3−i3−i3i300000000000000
χ846-6-66-300-6633-33i3−3i33i3−3i30−3i33i33-3000000000000000000000000000000000000002-200-1-1110000i3−i3−i3i300000000000000
χ856-6-66-300-6633-33i3−3i33i3−3i30−3i33i33-300000000000000000000000000000000000000-220011-1-10000−i3i3i3−i300000000000000
χ861212-12-12-612i−12i00-666−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-6−12i12i00-6666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-1212-12-600006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-1212-12-600006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000

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