Finite Group Databasebeta

← Group #13139953

Character table — Group #13139953

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222344446661212121226612123366666612121212366666666666121212121212121212121212121244448888121212121212121224242424242424244412121212
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
χ511111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-111
χ611111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1
χ711111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1
χ811111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-111
χ92222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-222-2-2-2-22222000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-1000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-10000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-111110000000000000000000000002-211-1-1
χ1922222-2-222222-2-2-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-11111000000000000000000000000-22-1-111
χ2022222-2-222222-2-2-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-11111000022-2-200000000-1-1-1-11111000000
χ2122222-2-222222-2-2-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-111110000-2-222000000001111-1-1-1-1000000
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
χ2322222-2-2-2-2222-2-2-2-2222-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-2222-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-2222-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-211111111000000000000000033−3−3−3−333000000
χ2622222-2-2-2-2222-2-2-2-2222-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-2111111110000000000000000−3−33333−3−3000000
χ272-22-22002-22-2-200000002-222-2-2-22-2222-2-220000-2-200002002-20022-2-20000002i−2i000000002i2i−2i−2i00000000000000
χ282-22-22002-22-2-200000002-222-2-2-22-2222-2-220000-2-200002002-20022-2-2000000−2i2i00000000−2i−2i2i2i00000000000000
χ292-22-2200-222-2-20000000-2222-2-2-22-22-2-22220000-2-20000200-2200-2-22200002i−2i0000002i2i−2i−2i000000000000000000
χ302-22-2200-222-2-20000000-2222-2-2-22-22-2-22220000-2-20000200-2200-2-2220000−2i2i000000−2i−2i2i2i000000000000000000
χ312-2-2222i−2i00-22-22i2i−2i−2i00000222-2-2-22-20000200002-20000-22i−2i002i−2i00002i2i−2i−2i00002−2−i2i2000000002−22−2−i2i2−i2i2000000
χ322-2-2222i−2i00-22-22i2i−2i−2i00000222-2-2-22-20000200002-20000-22i−2i002i−2i00002i2i−2i−2i0000−22i2−i200000000−22−22i2−i2i2−i2000000
χ332-2-2222i−2i00-22-22i2i−2i−2i00000-12-11-212-23−33−3-1−i3i300-11−i3−i3i3i31−ii002i−2i3−33−3−i−iii00002−2−i2i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ342-2-2222i−2i00-22-22i2i−2i−2i00000-12-11-212-23−33−3-1−i3i300-11−i3−i3i3i31−ii002i−2i3−33−3−i−iii0000−22i2−i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ352-2-2222i−2i00-22-22i2i−2i−2i00000-12-11-212-2−33−33-1i3−i300-11i3i3−i3−i31−ii002i−2i−33−33−i−iii00002−2−i2i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ362-2-2222i−2i00-22-22i2i−2i−2i00000-12-11-212-2−33−33-1i3−i300-11i3i3−i3−i31−ii002i−2i−33−33−i−iii0000−22i2−i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ372-2-222−2i2i00-22-2−2i−2i2i2i00000222-2-2-22-20000200002-20000-2−2i2i00−2i2i0000−2i−2i2i2i00002−2i2−i2000000002−22−2i2−i2i2−i2000000
χ382-2-222−2i2i00-22-2−2i−2i2i2i00000222-2-2-22-20000200002-20000-2−2i2i00−2i2i0000−2i−2i2i2i0000−22−i2i200000000−22−22−i2i2−i2i2000000
χ392-2-222−2i2i00-22-2−2i−2i2i2i00000-12-11-212-23−33−3-1i3−i300-11i3i3−i3−i31i−i00−2i2i3−33−3ii−i−i00002−2i2−i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ402-2-222−2i2i00-22-2−2i−2i2i2i00000-12-11-212-23−33−3-1i3−i300-11i3i3−i3−i31i−i00−2i2i3−33−3ii−i−i0000−22−i2i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ412-2-222−2i2i00-22-2−2i−2i2i2i00000-12-11-212-2−33−33-1−i3i300-11−i3−i3i3i31i−i00−2i2i−33−33ii−i−i00002−2i2−i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ422-2-222−2i2i00-22-2−2i−2i2i2i00000-12-11-212-2−33−33-1−i3i300-11−i3−i3i3i31i−i00−2i2i−33−33ii−i−i0000−22−i2i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4544444-4-444444-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000000000
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
χ4744-4-440000-4-4400000000044-444-4-4-4000040000-440000-400000000000000000000000000000000000000000000
χ4844-4-440000-4-440000000004-2-44-2-4220000-200−2i32i32-2−2i32i3−2i32i3200000000000000000000000000000000000000000000
χ4944-4-440000-4-440000000004-2-44-2-4220000-2002i3−2i32-22i3−2i32i3−2i3200000000000000000000000000000000000000000000
χ5044-4-440000-4-44000000000-242-242-4-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ5144-4-440000-4-44000000000-242-242-4-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ5244-4-440000-4-44000000000-2-22-2-222223−23−2323100−2i32i3-11i3−i3i3−i3-1000000−333−33i−3i3i−3i000000000000000000000000000000
χ5344-4-440000-4-44000000000-2-22-2-222223−23−23231002i3−2i3-11−i3i3−i3i3-1000000−333−3−3i3i−3i3i000000000000000000000000000000
χ5444-4-440000-4-44000000000-2-22-2-2222−232323−23100−2i32i3-11i3−i3i3−i3-10000003−3−33−3i3i−3i3i000000000000000000000000000000
χ5544-4-440000-4-44000000000-2-22-2-2222−232323−231002i3−2i3-11−i3i3−i3i3-10000003−3−333i−3i3i−3i000000000000000000000000000000
χ564-44-44004-44-4-400000004-44-2-4-4242-244-4-4-20000220000-200-2200-2-2220000000000000000000000000000000000
χ574-44-44004-44-4-400000004-4-2422-4-2-44-2-222-20000220000-2004-400-2-2220000000000000000000000000000000000
χ584-44-44004-44-4-400000004-4-2-2222-22-2-2-22210000-1-13-3-33100-220011-1-1-333-3000000000000000000000000000000
χ594-44-44004-44-4-400000004-4-2-2222-22-2-2-22210000-1-1-333-3100-220011-1-13-3-33000000000000000000000000000000
χ604-44-4400-444-4-40000000-444-2-4-4242-2-4-444-20000220000-2002-20022-2-20000000000000000000000000000000000
χ614-44-4400-444-4-40000000-44-2422-4-2-4422-2-2-20000220000-200-440022-2-20000000000000000000000000000000000
χ624-44-4400-444-4-40000000-44-2-2222-22-222-2-210000-1-13-3-331002-200-1-1113-3-33000000000000000000000000000000
χ634-44-4400-444-4-40000000-44-2-2222-22-222-2-210000-1-1-333-31002-200-1-111-333-3000000000000000000000000000000
χ644-4-4444i−4i00-44-44i4i−4i−4i000004-24-42-4-220000-20000-22000024i−4i00−2i2i0000−2i−2i2i2i000000000000000000000000000000
χ654-4-4444i−4i00-44-44i4i−4i−4i00000-2-2-2222-2223−2323−231−2i32i3001-1i3i3−i3−i3-1−2i2i00−2i2i−33−33ii−i−i000000000000000000000000000000
χ664-4-4444i−4i00-44-44i4i−4i−4i00000-2-2-2222-22−2323−232312i3−2i3001-1−i3−i3i3i3-1−2i2i00−2i2i3−33−3ii−i−i000000000000000000000000000000
χ674-4-444−4i4i00-44-4−4i−4i4i4i000004-24-42-4-220000-20000-2200002−4i4i002i−2i00002i2i−2i−2i000000000000000000000000000000
χ684-4-444−4i4i00-44-4−4i−4i4i4i00000-2-2-2222-2223−2323−2312i3−2i3001-1−i3−i3i3i3-12i−2i002i−2i−33−33−i−iii000000000000000000000000000000
χ694-4-444−4i4i00-44-4−4i−4i4i4i00000-2-2-2222-22−2323−23231−2i32i3001-1i3i3−i3−i3-12i−2i002i−2i3−33−3−i−iii000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-100000000000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-200001111111100000000000000
χ726666-366-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000000000
χ736666-366-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000000000
χ746666-3-6-666-3-3-33333-633-3-30000000000000000000000000000000000000022-2-20000-1-1-1-1111100000000000000
χ756666-3-6-666-3-3-33333-633-3-300000000000000000000000000000000000000-2-22200001111-1-1-1-100000000000000
χ766666-3-6-6-6-6-3-3-333336-3-3330000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i300000000000000
χ776666-3-6-6-6-6-3-3-333336-3-3330000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i300000000000000
χ786-66-6-3006-6-333−3i33i3−3i33i30−3i33i3-3300000000000000000000000000000000000000002i−2i00003−3−33−i−iii00000000000000
χ796-66-6-3006-6-333−3i33i3−3i33i30−3i33i3-330000000000000000000000000000000000000000−2i2i0000−333−3ii−i−i00000000000000
χ806-66-6-3006-6-3333i3−3i33i3−3i303i3−3i3-3300000000000000000000000000000000000000002i−2i0000−333−3−i−iii00000000000000
χ816-66-6-3006-6-3333i3−3i33i3−3i303i3−3i3-330000000000000000000000000000000000000000−2i2i00003−3−33ii−i−i00000000000000
χ826-66-6-300-66-333−3i33i3−3i33i303i3−3i33-3000000000000000000000000000000000000002i−2i000000−i−iii3−3−3300000000000000
χ836-66-6-300-66-333−3i33i3−3i33i303i3−3i33-300000000000000000000000000000000000000−2i2i000000ii−i−i−333−300000000000000
χ846-66-6-300-66-3333i3−3i33i3−3i30−3i33i33-3000000000000000000000000000000000000002i−2i000000−i−iii−333−300000000000000
χ856-66-6-300-66-3333i3−3i33i3−3i30−3i33i33-300000000000000000000000000000000000000−2i2i000000ii−i−i3−3−3300000000000000
χ861212-12-12-6000066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-6000066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-612i−12i006-66−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-6−12i12i006-666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000

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