Finite Group Databasebeta

← Group #13150721

Character table — Group #13150721

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12222234466612121212466121233666666666636666666661212121212121212121212121212121222444444224444446666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-11-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-11-11-1-1-1111111-1-111-1-1-1-11-11-1
χ61111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-11-11111111-1-111-1-1-1-1-1-1-11-11
χ71111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11-11-1-1-1-1-1-111-1-1111111-11-11
χ81111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-11-111-1-1-1-1-1-111-1-111111-11-1
χ91111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1111111-1-1-1-1-111-1-11-1-111-1-11111-1-111-1-11-1-11
χ101111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-111-11-1-1-111-11111-1-1-1-1-1-11111-1-1-111-1
χ111111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-111-1-11-111-111-1-1-1-1-1111111-1-1-1-111-111-1
χ121111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-11-1-1111-1-111-1-1-1-111-1-1111-1-11
χ131111-1-11-1-1111-1-1-1-11-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-111-1-1-111-111-1-11111-1-111-1-1-1-1-1-11111-1-1
χ141111-1-11-1-1111-1-1-1-11-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-111-1-111
χ151111-1-11-1-1111-1-1-1-11-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111
χ161111-1-11-1-1111-1-1-1-11-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111-1-1111-1-1111-1-1-1-1-1-111-1-1111111-1-111-1-1
χ172222222222222222222222-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200002020000000-1-1-1-1000000-1-1-1-10000
χ182222222222222222222222-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000-20-20000000111100000011110000
χ19222222222222222222222-12-1222222-12-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000022220000000000000000-1-1-1-1
χ20222222222222222222222-12-1222222-12-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000000001111
χ212222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-11111-2-2-2-21111111122-2-2000020-20000000-1-1-1-100000011110000
χ222222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-11111-2-2-2-211111111-2-2220000-20200000001111000000-1-1-1-10000
χ232222222-2-2222-2-2-2-2-222-2-2-12-1222222-12-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000000002-22-20000000000000000-11-11
χ242222222-2-2222-2-2-2-2-222-2-2-12-1222222-12-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000-22-2200000000000000001-11-1
χ252222-2-22222222222-2-2-2-2-22-12-11111-12-12-1-2-2-1-11111-1-1-11122-2-2-1-1-1-1111122220000-20-20000000-1-111000000-1-1110000
χ262222-2-22222222222-2-2-2-2-22-12-11111-12-12-1-2-2-1-11111-1-1-11122-2-2-1-1-1-11111-2-2-2-20000202000000011-1-100000011-1-10000
χ272222-2-22222222222-2-2-2-2-2-12-12-2-2-2-22-12-1-111-1-11111-122-2-2-1-111-1-1-1-111110000000000002-2-220000000000000000-111-1
χ282222-2-22222222222-2-2-2-2-2-12-12-2-2-2-22-12-1-111-1-11111-122-2-2-1-111-1-1-1-11111000000000000-222-200000000000000001-1-11
χ292222-2-22-2-2222-2-2-2-22-2-2222-12-11111-12-12-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-122-2-20000-2020000000-1-11100000011-1-10000
χ302222-2-22-2-2222-2-2-2-22-2-2222-12-11111-12-12-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-1-2-222000020-2000000011-1-1000000-1-1110000
χ312222-2-22-2-2222-2-2-2-22-2-222-12-12-2-2-2-22-12-1-111-1-11111-1-2-22211-1-11111-1-1-1-100000000000022-2-20000000000000000-1-111
χ322222-2-22-2-2222-2-2-2-22-2-222-12-12-2-2-2-22-12-1-111-1-11111-1-2-22211-1-11111-1-1-1-1000000000000-2-222000000000000000011-1-1
χ3322-2-20022i−2i2-2-22i2i−2i−2i0000022-220000-22-2-22002-20000-22i−2i002i−2i002i2i−2i−2i00002-22i−2i000000000000002-2000000002i−2i000000
χ3422-2-20022i−2i2-2-22i2i−2i−2i0000022-220000-22-2-22002-20000-22i−2i002i−2i002i2i−2i−2i0000-22−2i2i00000000000000-2200000000−2i2i000000
χ3522-2-20022i−2i2-2-22i2i−2i−2i000002-1-2-1−i3−i3i3i3121-2-100-11−i3−i3i3i31−ii3−32i−2i00−i−iii33−3−32-22i−2i00000000000000-11−i3i3000000−ii3−30000
χ3622-2-20022i−2i2-2-22i2i−2i−2i000002-1-2-1−i3−i3i3i3121-2-100-11−i3−i3i3i31−ii3−32i−2i00−i−iii33−3−3-22−2i2i000000000000001-1i3−i3000000i−i−330000
χ3722-2-20022i−2i2-2-22i2i−2i−2i000002-1-2-1i3i3−i3−i3121-2-100-11i3i3−i3−i31−ii−332i−2i00−i−iii−3−3332-22i−2i00000000000000-11i3−i3000000−ii−330000
χ3822-2-20022i−2i2-2-22i2i−2i−2i000002-1-2-1i3i3−i3−i3121-2-100-11i3i3−i3−i31−ii−332i−2i00−i−iii−3−333-22−2i2i000000000000001-1−i3i3000000i−i3−30000
χ3922-2-2002−2i2i2-2-2−2i−2i2i2i0000022-220000-22-2-22002-20000-2−2i2i00−2i2i00−2i−2i2i2i00002-2−2i2i000000000000002-200000000−2i2i000000
χ4022-2-2002−2i2i2-2-2−2i−2i2i2i0000022-220000-22-2-22002-20000-2−2i2i00−2i2i00−2i−2i2i2i0000-222i−2i00000000000000-22000000002i−2i000000
χ4122-2-2002−2i2i2-2-2−2i−2i2i2i000002-1-2-1−i3−i3i3i3121-2-100-11−i3−i3i3i31i−i−33−2i2i00ii−i−i−3−3332-2−2i2i00000000000000-11−i3i3000000i−i−330000
χ4222-2-2002−2i2i2-2-2−2i−2i2i2i000002-1-2-1−i3−i3i3i3121-2-100-11−i3−i3i3i31i−i−33−2i2i00ii−i−i−3−333-222i−2i000000000000001-1i3−i3000000−ii3−30000
χ4322-2-2002−2i2i2-2-2−2i−2i2i2i000002-1-2-1i3i3−i3−i3121-2-100-11i3i3−i3−i31i−i3−3−2i2i00ii−i−i33−3−32-2−2i2i00000000000000-11i3−i3000000i−i3−30000
χ4422-2-2002−2i2i2-2-2−2i−2i2i2i000002-1-2-1i3i3−i3−i3121-2-100-11i3i3−i3−i31i−i3−3−2i2i00ii−i−i33−3−3-222i−2i000000000000001-1−i3i3000000−ii−330000
χ452-22-22-2200-22-2000002-200222-22-22-2-2-22-222-2-222-22-2-2000000000000000000002i−2i2i−2i000000000000002i−2i002i−2i00000000
χ462-22-22-2200-22-2000002-200222-22-22-2-2-22-222-2-222-22-2-200000000000000000000−2i2i−2i2i00000000000000−2i2i00−2i2i00000000
χ472-22-2-22200-22-200000-2200222-2-22-22-2-22-22-22-22-22-22-2000000000000000000002i−2i−2i2i000000000000002i−2i00−2i2i00000000
χ482-22-2-22200-22-200000-2200222-2-22-22-2-22-22-22-22-22-22-200000000000000000000−2i2i2i−2i00000000000000−2i2i002i−2i00000000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ504444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ514444-4-44444444444-4-4-4-4-4-2-2-2-22222-2-2-2-212211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000000000
χ524444-4-44-4-4444-4-4-4-44-4-444-2-2-2-22222-2-2-2-212211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5344-4-40044i−4i4-4-44i4i−4i−4i00000-24240000-4-2-42-200-22000024i−4i00−2i2i00−2i−2i2i2i0000000000000000000000000000000000000000
χ5444-4-40044i−4i4-4-44i4i−4i−4i00000-2-22-2−2i3−2i32i32i32-2221001-1i3i3−i3−i3-1−2i2i23−23−2i2i00ii−i−i−3−333000000000000000000000000000000000000
χ5544-4-40044i−4i4-4-44i4i−4i−4i00000-2-22-22i32i3−2i3−2i32-2221001-1−i3−i3i3i3-1−2i2i−2323−2i2i00ii−i−i33−3−3000000000000000000000000000000000000
χ5644-4-4004−4i4i4-4-4−4i−4i4i4i00000-24240000-4-2-42-200-2200002−4i4i002i−2i002i2i−2i−2i0000000000000000000000000000000000000000
χ5744-4-4004−4i4i4-4-4−4i−4i4i4i00000-2-22-2−2i3−2i32i32i32-2221001-1i3i3−i3−i3-12i−2i−23232i−2i00−i−iii33−3−3000000000000000000000000000000000000
χ5844-4-4004−4i4i4-4-4−4i−4i4i4i00000-2-22-22i32i3−2i3−2i32-2221001-1−i3−i3i3i3-12i−2i23−232i−2i00−i−iii−3−333000000000000000000000000000000000000
χ594-44-44-4400-44-4000004-4004-242-22-222-4-2-4-24-42-2-22-2220000000000000000000000000000000000000000000000000000
χ604-44-44-4400-44-4000004-400-24-2-44-44-4-4242-2-222-2-22-2220000000000000000000000000000000000000000000000000000
χ614-44-44-4400-44-4000004-400-2-2-22-22-2222-221-22-111-11-1-1000000003i−3i3i−3i3i−3i3i−3i000000000000000000000000000000000000
χ624-44-44-4400-44-4000004-400-2-2-22-22-2222-221-22-111-11-1-100000000−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000000000
χ634-44-4-44400-44-400000-44004-2422-22-22-4-2-4-2-442-22-22-220000000000000000000000000000000000000000000000000000
χ644-44-4-44400-44-400000-4400-24-2-4-44-44-4242-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ654-44-4-44400-44-400000-4400-2-2-222-22-222-2212-2-11-11-11-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ664-44-4-44400-44-400000-4400-2-2-222-22-222-2212-2-11-11-11-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ674-4-4400400-4-4400000000044-4-400004-4-44400-4-4000040000000000000000000000000000000000000000000000000000
χ684-4-4400400-4-440000000004-2-42−2i32i32i3−2i3-2-424-20022−2i32i32i3−2i3-20000000000000000000000000000000000000000000000000000
χ694-4-4400400-4-440000000004-2-422i3−2i3−2i32i3-2-424-200222i3−2i3−2i32i3-20000000000000000000000000000000000000000000000000000
χ704-4-4400400-4-44000000000-242-4000042-4-2-200220000-2000000−2i32i30000−2i32i32i3−2i3000000000000000000000000000000000000
χ714-4-4400400-4-44000000000-242-4000042-4-2-200220000-20000002i3−2i300002i3−2i3−2i32i3000000000000000000000000000000000000
χ724-4-4400400-4-44000000000-2-222−2i32i32i3−2i3-222-2100-1-1i3−i3−i3i31000000−2i32i3-333-3i3−i3−i3i3000000000000000000000000000000000000
χ734-4-4400400-4-44000000000-2-222−2i32i32i3−2i3-222-2100-1-1i3−i3−i3i310000002i3−2i33-3-33−i3i3i3−i3000000000000000000000000000000000000
χ744-4-4400400-4-44000000000-2-2222i3−2i3−2i32i3-222-2100-1-1−i3i3i3−i31000000−2i32i33-3-33i3−i3−i3i3000000000000000000000000000000000000
χ754-4-4400400-4-44000000000-2-2222i3−2i3−2i32i3-222-2100-1-1−i3i3i3−i310000002i3−2i3-333-3−i3i3i3−i3000000000000000000000000000000000000
χ76666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222202020000-1-10000-1-1-1-1-1-100000000
χ77666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-20-20-2000011000011111100000000
χ78666666-3-6-6-3-3-33333-6-3-33300000000000000000000000000000000000000000022220-20-20000110000-1-111-1-100000000
χ79666666-3-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000-2-2-2-202020000-1-1000011-1-11100000000
χ806666-6-6-366-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-20-2020000110000-1-1-1-11100000000
χ816666-6-6-366-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222020-20000-1-100001111-1-100000000
χ826666-6-6-3-6-6-3-3-33333633-3-300000000000000000000000000000000000000000022-2-2020-20000-1-10000-1-1111100000000
χ836666-6-6-3-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000-2-2220-202000011000011-1-1-1-100000000
χ846-66-66-6-3003-3333−3333−330-3333−330000000000000000000000000000000000000000002i−2i2i−2i00000000−i3i30000−ii−i3i3−ii00000000
χ856-66-66-6-3003-3333−3333−330-3333−33000000000000000000000000000000000000000000−2i2i−2i2i00000000i3−i30000i−ii3−i3i−i00000000
χ866-66-66-6-3003-33−3333−33330-33−33330000000000000000000000000000000000000000002i−2i2i−2i00000000i3−i30000−iii3−i3−ii00000000
χ876-66-66-6-3003-33−3333−33330-33−3333000000000000000000000000000000000000000000−2i2i−2i2i00000000−i3i30000i−i−i3i3i−i00000000
χ886-66-6-66-3003-3333−3333−3303-3−33330000000000000000000000000000000000000000002i−2i−2i2i00000000i3−i30000−ii−i3i3i−i00000000
χ896-66-6-66-3003-3333−3333−3303-3−3333000000000000000000000000000000000000000000−2i2i2i−2i00000000−i3i30000i−ii3−i3−ii00000000
χ906-66-6-66-3003-33−3333−333303-333−330000000000000000000000000000000000000000002i−2i−2i2i00000000−i3i30000−iii3−i3i−i00000000
χ916-66-6-66-3003-33−3333−333303-333−33000000000000000000000000000000000000000000−2i2i2i−2i00000000i3−i30000i−i−i3i3−ii00000000
χ921212-12-1200-612i−12i-666−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-1200-6−12i12i-6666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-60066-6−6i36i36i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-60066-66i3−6i3−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).