Finite Group Databasebeta

← Group #13150748

Character table — Group #13150748

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222223446661212121246612123366666666663666666666121212121212121212121212121212124444444422244444661212121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-11-11-1-1-111-1-1111111-1-1-1-11-11-1
χ61111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-11-11-1-111-1-111-1-1-1-11111-11-11
χ71111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-111-111-1-111-1-11111-1-1-1-1-11-11
χ81111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1111-1-111-1-1-1-1-1-111111-11-1
χ91111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-111111-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-111
χ101111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ111111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1111111-1111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ121111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-11111-1-1-1-111-1-111-1-111
χ131111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1111-1-11-1-1-1-1111111-1-1-1-111-111-1
χ141111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1-1-111-11-11-111-1-1-1-1-11111-1-11111-1-11-1-11
χ151111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-11-111111-1-1-1-111-1-1-1-1111-1-11
χ161111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-11-11-11111-1-1-1-1-1-11111-1-1-111-1
χ172222222222222222222222-122222-12-1-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000022022000000000000000000-1-1-1-1
χ182222222222222222222222-122222-12-1-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000000000-2-20-2-20000000000000000001111
χ19222222222222222222222-12-1-1-1-1-12-122-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000022220000002200000000-1-1-1-1-1-1-1-10000
χ20222222222222222222222-12-1-1-1-1-12-122-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000111111110000
χ212222222-2-2222-2-2-2-2-222-2-22-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000000002-202-2000000000000000000-11-11
χ222222222-2-2222-2-2-2-2-222-2-22-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-2-211-2-21111111111000000000-220-220000000000000000001-11-1
χ232222222-2-2222-2-2-2-2-222-2-2-12-1-1-1-1-12-122-1-122-1-1-1-1-1-1-111-2-211-2-211111111000022-2-20000002-200000000-1-1-1-111110000
χ242222222-2-2222-2-2-2-2-222-2-2-12-1-1-1-1-12-122-1-122-1-1-1-1-1-1-111-2-211-2-2111111110000-2-222000000-22000000001111-1-1-1-10000
χ252222-2-22222222222-2-2-2-2-22-12-2-2-2-2-12-1-12-111-1-11111-122-1-1-2-211-1-1-1-11111000000000220-2-2000000000000000000-1-111
χ262222-2-22222222222-2-2-2-2-22-12-2-2-2-2-12-1-12-111-1-11111-122-1-1-2-211-1-1-1-11111000000000-2-202200000000000000000011-1-1
χ272222-2-22222222222-2-2-2-2-2-12-111112-122-1-1-2-2-1-11111-1-1-12211-2-2-1-1-1-1111100002222000000-2-200000000-1-111-1-1110000
χ282222-2-22222222222-2-2-2-2-2-12-111112-122-1-1-2-2-1-11111-1-1-12211-2-2-1-1-1-111110000-2-2-2-2000000220000000011-1-111-1-10000
χ292222-2-22-2-2222-2-2-2-22-2-2222-12-2-2-2-2-12-1-12-111-1-11111-1-2-21122-1-11111-1-1-1-10000000002-20-22000000000000000000-111-1
χ302222-2-22-2-2222-2-2-2-22-2-2222-12-2-2-2-2-12-1-12-111-1-11111-1-2-21122-1-11111-1-1-1-1000000000-2202-20000000000000000001-1-11
χ312222-2-22-2-2222-2-2-2-22-2-222-12-111112-122-1-1-2-2-1-11111-111-2-2-1-1221111-1-1-1-1000022-2-2000000-2200000000-1-11111-1-10000
χ322222-2-22-2-2222-2-2-2-22-2-222-12-111112-122-1-1-2-2-1-11111-111-2-2-1-1221111-1-1-1-10000-2-2220000002-20000000011-1-1-1-1110000
χ3322-2-20022-2-2-2222-2-20000022-20000-222-2-2200-2-2000022-22-2000022-2-2000000002i−2i2i−2i00000000000000002i−2i002i−2i000000
χ3422-2-20022-2-2-2222-2-20000022-20000-222-2-2200-2-2000022-22-2000022-2-200000000−2i2i−2i2i0000000000000000−2i2i00−2i2i000000
χ3522-2-20022-2-2-2222-2-200000-121−i3−i3i3i3-2-12-21-10011−i3−i3i3i3-1-112-2−i3i300-1-111−i3−i3i3i300002i−2i2i−2i0000000000000000−ii3−3−ii3−30000
χ3622-2-20022-2-2-2222-2-200000-121−i3−i3i3i3-2-12-21-10011−i3−i3i3i3-1-112-2−i3i300-1-111−i3−i3i3i30000−2i2i−2i2i0000000000000000i−i−33i−i−330000
χ3722-2-20022-2-2-2222-2-200000-121i3i3−i3−i3-2-12-21-10011i3i3−i3−i3-1-112-2i3−i300-1-111i3i3−i3−i300002i−2i2i−2i0000000000000000−ii−33−ii−330000
χ3822-2-20022-2-2-2222-2-200000-121i3i3−i3−i3-2-12-21-10011i3i3−i3−i3-1-112-2i3−i300-1-111i3i3−i3−i30000−2i2i−2i2i0000000000000000i−i3−3i−i3−30000
χ3922-2-2002-22-2-22-2-2220000022-20000-222-2-2200-2-200002-22-220000-2-222000000002i−2i−2i2i00000000000000002i−2i00−2i2i000000
χ4022-2-2002-22-2-22-2-2220000022-20000-222-2-2200-2-200002-22-220000-2-22200000000−2i2i2i−2i0000000000000000−2i2i002i−2i000000
χ4122-2-2002-22-2-22-2-22200000-121−i3−i3i3i3-2-12-21-10011−i3−i3i3i3-11-1-22i3−i30011-1-1i3i3−i3−i300002i−2i−2i2i0000000000000000−ii3−3i−i−330000
χ4222-2-2002-22-2-22-2-22200000-121−i3−i3i3i3-2-12-21-10011−i3−i3i3i3-11-1-22i3−i30011-1-1i3i3−i3−i30000−2i2i2i−2i0000000000000000i−i−33−ii3−30000
χ4322-2-2002-22-2-22-2-22200000-121i3i3−i3−i3-2-12-21-10011i3i3−i3−i3-11-1-22−i3i30011-1-1−i3−i3i3i300002i−2i−2i2i0000000000000000−ii−33i−i3−30000
χ4422-2-2002-22-2-22-2-22200000-121i3i3−i3−i3-2-12-21-10011i3i3−i3−i3-11-1-22−i3i30011-1-1−i3−i3i3i30000−2i2i2i−2i0000000000000000i−i3−3−ii−330000
χ452-22-22-22002-2-2000002-2002222-22-2-2-2-22-222-22-22-22-2-200000000000000002i−2i2i−2i000000000000002i−2i002i−2i000000000000
χ462-22-22-22002-2-2000002-2002222-22-2-2-2-22-222-22-22-22-2-20000000000000000−2i2i−2i2i00000000000000−2i2i00−2i2i000000000000
χ472-22-2-222002-2-200000-2200222-22-22-2-2-22-22-222-2-22-22-200000000000000002i−2i−2i2i00000000000000−2i2i002i−2i000000000000
χ482-22-2-222002-2-200000-2200222-22-22-2-2-22-22-222-2-22-22-20000000000000000−2i2i2i−2i000000000000002i−2i00−2i2i000000000000
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
χ514444-4-44444444444-4-4-4-4-4-2-2-22222-2-2-2-2-212211-1-1-1-11-2-2-2-222221111-1-1-1-1000000000000000000000000000000000000
χ524444-4-44-4-4444-4-4-4-44-4-444-2-2-22222-2-2-2-2-212211-1-1-1-112222-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ5344-4-40044-4-4-4444-4-4000004-2-4000024-22-4-200220000-24-4-220000-2-2220000000000000000000000000000000000000000
χ5444-4-40044-4-4-4444-4-400000-2-22−2i3−2i32i32i32-2-222100-1-1i3i3−i3−i31-22-22−2i32i30011-1-1i3i3−i3−i3000000000000000000000000000000000000
χ5544-4-40044-4-4-4444-4-400000-2-222i32i3−2i3−2i32-2-222100-1-1−i3−i3i3i31-22-222i3−2i30011-1-1−i3−i3i3i3000000000000000000000000000000000000
χ5644-4-4004-44-4-44-4-444000004-2-4000024-22-4-200220000-2-442-2000022-2-20000000000000000000000000000000000000000
χ5744-4-4004-44-4-44-4-44400000-2-22−2i3−2i32i32i32-2-222100-1-1i3i3−i3−i312-22-22i3−2i300-1-111−i3−i3i3i3000000000000000000000000000000000000
χ5844-4-4004-44-4-44-4-44400000-2-222i32i3−2i3−2i32-2-222100-1-1−i3−i3i3i312-22-2−2i32i300-1-111i3i3−i3−i3000000000000000000000000000000000000
χ594-44-44-44004-4-4000004-4004-244-44-42-42-2-4-2-22-22-22-2220000000000000000000000000000000000000000000000000000
χ604-44-44-44004-4-4000004-400-24-2-22-22-42-442-24-4-22-22-2220000000000000000000000000000000000000000000000000000
χ614-44-44-44004-4-4000004-400-2-2-2-22-22222-221-221-11-11-1-1000000003i−3i3i−3i3i−3i3i−3i000000000000000000000000000000000000
χ624-44-44-44004-4-4000004-400-2-2-2-22-22222-221-221-11-11-1-100000000−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000000000
χ634-44-4-444004-4-400000-44004-24-44-442-42-2-4-22-2-222-22-220000000000000000000000000000000000000000000000000000
χ644-44-4-444004-4-400000-4400-24-22-22-2-42-442-2-44-222-22-220000000000000000000000000000000000000000000000000000
χ654-44-4-444004-4-400000-4400-2-2-22-22-2222-2212-21-1-11-11-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ664-44-4-444004-4-400000-4400-2-2-22-22-2222-2212-21-1-11-11-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ674-4-4400400-44-400000000044-400004-4-4-44400-440000-40000000000000000000000000000000000000000000000000000
χ684-4-4400400-44-40000000004-2-40000-2-4224-2002-20000200000023−23000023−23−2323000000000000000000000000000000000000
χ694-4-4400400-44-40000000004-2-40000-2-4224-2002-200002000000−23230000−232323−23000000000000000000000000000000000000
χ704-4-4400400-44-4000000000-242−2i32i32i3−2i342-4-4-2-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000000000
χ714-4-4400400-44-4000000000-2422i3−2i3−2i32i342-4-4-2-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000000000
χ724-4-4400400-44-4000000000-2-22−2i32i32i3−2i3-2222-2100-11i3−i3−i3i3-100000023−23−3i3i3i−3i−333−3000000000000000000000000000000000000
χ734-4-4400400-44-4000000000-2-22−2i32i32i3−2i3-2222-2100-11i3−i3−i3i3-1000000−23233i−3i−3i3i3−3−33000000000000000000000000000000000000
χ744-4-4400400-44-4000000000-2-222i3−2i3−2i32i3-2222-2100-11−i3i3i3−i3-100000023−233i−3i−3i3i−333−3000000000000000000000000000000000000
χ754-4-4400400-44-4000000000-2-222i3−2i3−2i32i3-2222-2100-11−i3i3i3−i3-1000000−2323−3i3i3i−3i3−3−33000000000000000000000000000000000000
χ76666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002222000020020000-1-1-1-1-1-1-1-1000000000000
χ77666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-20000-200-2000011111111000000000000
χ78666666-3-6-6-3-3-33333-6-3-3330000000000000000000000000000000000000022220000-200-2000011-1-111-1-1000000000000
χ79666666-3-6-6-3-3-33333-6-3-33300000000000000000000000000000000000000-2-2-2-2000020020000-1-111-1-111000000000000
χ806666-6-6-366-3-3-3-3-3-3-3-633330000000000000000000000000000000000000022-2-20000200-20000-1-11111-1-1000000000000
χ816666-6-6-366-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000-2-2220000-2002000011-1-1-1-111000000000000
χ826666-6-6-3-6-6-3-3-33333633-3-30000000000000000000000000000000000000022-2-20000-200200001111-1-1-1-1000000000000
χ836666-6-6-3-6-6-3-3-33333633-3-300000000000000000000000000000000000000-2-2220000200-20000-1-1-1-11111000000000000
χ846-66-66-6-300-33333−3333−330-3333−33000000000000000000000000000000000000002i−2i2i−2i000000000000−i3i3−ii−i3i3−ii000000000000
χ856-66-66-6-300-33333−3333−330-3333−3300000000000000000000000000000000000000−2i2i−2i2i000000000000i3−i3i−ii3−i3i−i000000000000
χ866-66-66-6-300-333−3333−33330-33−3333000000000000000000000000000000000000002i−2i2i−2i000000000000i3−i3−iii3−i3−ii000000000000
χ876-66-66-6-300-333−3333−33330-33−333300000000000000000000000000000000000000−2i2i−2i2i000000000000−i3i3i−i−i3i3i−i000000000000
χ886-66-6-66-300-33333−3333−3303-3−3333000000000000000000000000000000000000002i−2i−2i2i000000000000−i3i3i−ii3−i3−ii000000000000
χ896-66-6-66-300-33333−3333−3303-3−333300000000000000000000000000000000000000−2i2i2i−2i000000000000i3−i3−ii−i3i3i−i000000000000
χ906-66-6-66-300-333−3333−333303-333−33000000000000000000000000000000000000002i−2i−2i2i000000000000i3−i3i−i−i3i3−ii000000000000
χ916-66-6-66-300-333−3333−333303-333−3300000000000000000000000000000000000000−2i2i2i−2i000000000000−i3i3−iii3−i3i−i000000000000
χ921212-12-1200-612-1266-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-1200-6-121266-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-6006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-6006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000000000

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