Finite Group Databasebeta

← Group #13150728

Character table — Group #13150728

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222223446661212121246612123366666666663666666666121212121212121212121212121212124444444424444444121212121212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-11-1-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-11111-111-1
χ61111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-11-11-11111-1-1-1-11111-1-1-1-11-1-11
χ71111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ81111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-111111111-1-1-1-1-111-1
χ91111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1111-1-111-1-111-1-111-1-1-11-11
χ101111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1-1-1-1-11-111-111-111-1-111-1-1-1-111-1-1111-11-1
χ111111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-111-1-11111-1-111-1-11-11-1
χ121111-1-11111111111-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-11-111-111-1-111-1-111-1-111-1-111-11-11
χ131111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1
χ141111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-111-11111-1-1-111-1-1-1-11111-1-1-1-111-1-111
χ151111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-11111-1-1-1-11-1111-1-1-11111-1-1-1-11111-1-1-1-111
χ161111-1-11-1-1111-1-1-1-11-1-111111-1-1-1-1111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111-1-11-11-11-1-11111-1-111-1-1-1-11111-1-1
χ172222222222222222222222-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000202020020000000000000000-1-1-1-1
χ182222222222222222222222-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-20-20-200-200000000000000001111
χ19222222222222222222222-12-1-1-1-1-1222-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002200220002002000000000-1-1-1-1-1-1-1-10000
χ20222222222222222222222-12-1-1-1-1-1222-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-2000-200-2000000000111111110000
χ212222222-2-2222-2-2-2-2-222-2-22-122222-1-1-122-1-1-1-1-1-1-1-1-1-11111-2-2-2-2111111110000000020-20200-20000000000000000-111-1
χ222222222-2-2222-2-2-2-2-222-2-22-122222-1-1-122-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2020-200200000000000000001-1-11
χ232222222-2-2222-2-2-2-2-222-2-2-12-1-1-1-1-1222-1-1-122-1-1-1-1-1-1-1-2-2-2-2111111111111002200-2-2000200-20000000001111-1-1-1-10000
χ242222222-2-2222-2-2-2-2-222-2-2-12-1-1-1-1-1222-1-1-122-1-1-1-1-1-1-1-2-2-2-211111111111100-2-20022000-2002000000000-1-1-1-111110000
χ252222-2-22222222222-2-2-2-2-22-12-2-2-2-2-1-1-122-111-1-11111-1-1-11122-2-2-1-1-1-11111000000002020-200-20000000000000000-11-11
χ262222-2-22222222222-2-2-2-2-22-12-2-2-2-2-1-1-122-111-1-11111-1-1-11122-2-2-1-1-1-1111100000000-20-20200200000000000000001-11-1
χ272222-2-22222222222-2-2-2-2-2-12-11111222-1-1-1-2-2-1-11111-122-2-2-1-111-1-1-1-1111100220022000-200-2000000000-1-111-1-1110000
χ282222-2-22222222222-2-2-2-2-2-12-11111222-1-1-1-2-2-1-11111-122-2-2-1-111-1-1-1-1111100-2-200-2-2000200200000000011-1-111-1-10000
χ292222-2-22-2-2222-2-2-2-22-2-2222-12-2-2-2-2-1-1-122-111-1-11111-111-1-1-2-2221111-1-1-1-10000000020-20-20020000000000000000-1-111
χ302222-2-22-2-2222-2-2-2-22-2-2222-12-2-2-2-2-1-1-122-111-1-11111-111-1-1-2-2221111-1-1-1-100000000-2020200-2000000000000000011-1-1
χ312222-2-22-2-2222-2-2-2-22-2-222-12-11111222-1-1-1-2-2-1-11111-1-2-22211-1-11111-1-1-1-1002200-2-2000-200200000000011-1-1-1-1110000
χ322222-2-22-2-2222-2-2-2-22-2-222-12-11111222-1-1-1-2-2-1-11111-1-2-22211-1-11111-1-1-1-100-2-20022000200-2000000000-1-11111-1-10000
χ332-22-22-22002-2-2000002-20022-222-2-2-2-22-2222-2-2-222-2-2200000000000000002i−2i002i−2i00000000002i−2i2i−2i0000000000000000
χ342-22-22-22002-2-2000002-20022-222-2-2-2-22-2222-2-2-222-2-220000000000000000−2i2i00−2i2i0000000000−2i2i−2i2i0000000000000000
χ352-22-2-222002-2-200000-220022-2-2-222-2-22-222-22-2-2-2-222200000000000000002i−2i00−2i2i00000000002i−2i−2i2i0000000000000000
χ362-22-2-222002-2-200000-220022-2-2-222-2-22-222-22-2-2-2-22220000000000000000−2i2i002i−2i0000000000−2i2i2i−2i0000000000000000
χ372-2-220022i−2i-22-22i2i−2i−2i0000022-200002-2-22-22002-20000-22i−2i002i−2i002i2i−2i−2i0000002i−2i002-200000000000000002-2002i−2i000000
χ382-2-220022i−2i-22-22i2i−2i−2i0000022-200002-2-22-22002-20000-22i−2i002i−2i002i2i−2i−2i000000−2i2i00-220000000000000000-2200−2i2i000000
χ392-2-220022i−2i-22-22i2i−2i−2i00000-121−i3i3−i3i32-2-2-11-100-11−i3i3−i3i312i−2i00−ii3−3−i−iii33−3−3002i−2i002-20000000000000000-11−i3i3−ii3−30000
χ402-2-220022i−2i-22-22i2i−2i−2i00000-121−i3i3−i3i32-2-2-11-100-11−i3i3−i3i312i−2i00−ii3−3−i−iii33−3−300−2i2i00-2200000000000000001-1i3−i3i−i−330000
χ412-2-220022i−2i-22-22i2i−2i−2i00000-121i3−i3i3−i32-2-2-11-100-11i3−i3i3−i312i−2i00−ii−33−i−iii−3−333002i−2i002-20000000000000000-11i3−i3−ii−330000
χ422-2-220022i−2i-22-22i2i−2i−2i00000-121i3−i3i3−i32-2-2-11-100-11i3−i3i3−i312i−2i00−ii−33−i−iii−3−33300−2i2i00-2200000000000000001-1−i3i3i−i3−30000
χ432-2-22002−2i2i-22-2−2i−2i2i2i0000022-200002-2-22-22002-20000-2−2i2i00−2i2i00−2i−2i2i2i0000002i−2i00-220000000000000000-22002i−2i000000
χ442-2-22002−2i2i-22-2−2i−2i2i2i0000022-200002-2-22-22002-20000-2−2i2i00−2i2i00−2i−2i2i2i000000−2i2i002-200000000000000002-200−2i2i000000
χ452-2-22002−2i2i-22-2−2i−2i2i2i00000-121−i3i3−i3i32-2-2-11-100-11−i3i3−i3i31−2i2i00i−i−33ii−i−i−3−333002i−2i00-2200000000000000001-1i3−i3−ii3−30000
χ462-2-22002−2i2i-22-2−2i−2i2i2i00000-121−i3i3−i3i32-2-2-11-100-11−i3i3−i3i31−2i2i00i−i−33ii−i−i−3−33300−2i2i002-20000000000000000-11−i3i3i−i−330000
χ472-2-22002−2i2i-22-2−2i−2i2i2i00000-121i3−i3i3−i32-2-2-11-100-11i3−i3i3−i31−2i2i00i−i3−3ii−i−i33−3−3002i−2i00-2200000000000000001-1−i3i3−ii−330000
χ482-2-22002−2i2i-22-2−2i−2i2i2i00000-121i3−i3i3−i32-2-2-11-100-11i3−i3i3−i31−2i2i00i−i3−3ii−i−i33−3−300−2i2i002-20000000000000000-11i3−i3i−i3−30000
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
χ514444-4-44444444444-4-4-4-4-4-2-2-22222-2-2-2-2-212211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000000000
χ524444-4-44-4-4444-4-4-4-44-4-444-2-2-22222-2-2-2-2-212211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5344-4-400400-4-440000000004440000-44-4-4-4400-440000-40000000000000000000000000000000000000000000000000000
χ5444-4-400400-4-440000000004-2400002-22-4-4-2002-2000020023−230000000023−2323−23000000000000000000000000000000000000
χ5544-4-400400-4-440000000004-2400002-22-4-4-2002-20000200−232300000000−2323−2323000000000000000000000000000000000000
χ5644-4-400400-4-44000000000-24-2−2i32i32i3−2i3-44-422-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000000000
χ5744-4-400400-4-44000000000-24-22i3−2i3−2i32i3-44-422-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000000000
χ5844-4-400400-4-44000000000-2-2-2−2i32i32i3−2i32-2222100-11i3−i3−i3i3-10023−2300003i−3i3i−3i−33−33000000000000000000000000000000000000
χ5944-4-400400-4-44000000000-2-2-2−2i32i32i3−2i32-2222100-11i3−i3−i3i3-100−23230000−3i3i−3i3i3−33−3000000000000000000000000000000000000
χ6044-4-400400-4-44000000000-2-2-22i3−2i3−2i32i32-2222100-11−i3i3i3−i3-10023−230000−3i3i−3i3i−33−33000000000000000000000000000000000000
χ6144-4-400400-4-44000000000-2-2-22i3−2i3−2i32i32-2222100-11−i3i3i3−i3-100−232300003i−3i3i−3i3−33−3000000000000000000000000000000000000
χ624-44-44-44004-4-4000004-4004-2-444-4-422-2-44-2-2222-2-222-20000000000000000000000000000000000000000000000000000
χ634-44-44-44004-4-4000004-400-242-2-222-4-442-2-24-422-2-222-20000000000000000000000000000000000000000000000000000
χ644-44-44-44004-4-4000004-400-2-22-2-22222-22-21-22-1-111-1-11000000003-3-33-333-3000000000000000000000000000000000000
χ654-44-44-44004-4-4000004-400-2-22-2-22222-22-21-22-1-111-1-1100000000-333-33-3-33000000000000000000000000000000000000
χ664-44-4-444004-4-400000-44004-2-4-4-44422-2-44-22-22222-2-2-20000000000000000000000000000000000000000000000000000
χ674-44-4-444004-4-400000-4400-24222-2-2-4-442-2-2-442222-2-2-20000000000000000000000000000000000000000000000000000
χ684-44-4-444004-4-400000-4400-2-2222-2-222-22-212-2-1-1-1-1111000000003-3-333-3-33000000000000000000000000000000000000
χ694-44-4-444004-4-400000-4400-2-2222-2-222-22-212-2-1-1-1-111100000000-333-3-333-3000000000000000000000000000000000000
χ704-4-440044i−4i-44-44i4i−4i−4i000004-2-40000-2224-4-200-2200002−2i2i004i−4i00−2i−2i2i2i0000000000000000000000000000000000000000
χ714-4-440044i−4i-44-44i4i−4i−4i00000-2-22−2i32i3−2i32i3-222-221001-1i3−i3i3−i3-1−2i2i00−2i2i23−23ii−i−i−3−333000000000000000000000000000000000000
χ724-4-440044i−4i-44-44i4i−4i−4i00000-2-222i3−2i32i3−2i3-222-221001-1−i3i3−i3i3-1−2i2i00−2i2i−2323ii−i−i33−3−3000000000000000000000000000000000000
χ734-4-44004−4i4i-44-4−4i−4i4i4i000004-2-40000-2224-4-200-22000022i−2i00−4i4i002i2i−2i−2i0000000000000000000000000000000000000000
χ744-4-44004−4i4i-44-4−4i−4i4i4i00000-2-22−2i32i3−2i32i3-222-221001-1i3−i3i3−i3-12i−2i002i−2i−2323−i−iii33−3−3000000000000000000000000000000000000
χ754-4-44004−4i4i-44-4−4i−4i4i4i00000-2-222i3−2i32i3−2i3-222-221001-1−i3i3−i3i3-12i−2i002i−2i23−23−i−iii−3−333000000000000000000000000000000000000
χ76666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002200220002000200-1-1-1-1-1-1-1-1000000000000
χ77666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-200-2-2000-2000-20011111111000000000000
χ78666666-3-6-6-3-3-33333-6-3-33300000000000000000000000000000000000000220022000-2000-200-1-1-1-11111000000000000
χ79666666-3-6-6-3-3-33333-6-3-33300000000000000000000000000000000000000-2-200-2-200020002001111-1-1-1-1000000000000
χ806666-6-6-366-3-3-3-3-3-3-3-63333000000000000000000000000000000000000002200-2-2000-2000200-1-111-1-111000000000000
χ816666-6-6-366-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000-2-200220002000-20011-1-111-1-1000000000000
χ826666-6-6-3-6-6-3-3-33333633-3-3000000000000000000000000000000000000002200-2-20002000-200-1-11111-1-1000000000000
χ836666-6-6-3-6-6-3-3-33333633-3-300000000000000000000000000000000000000-2-20022000-200020011-1-1-1-111000000000000
χ846-66-66-6-300-333−3i33i3−3i33i30-33−3i33i3000000000000000000000000000000000000002i−2i002i−2i0000000000−ii−ii3−33−3000000000000
χ856-66-66-6-300-333−3i33i3−3i33i30-33−3i33i300000000000000000000000000000000000000−2i2i00−2i2i0000000000i−ii−i−33−33000000000000
χ866-66-66-6-300-3333i3−3i33i3−3i30-333i3−3i3000000000000000000000000000000000000002i−2i002i−2i0000000000−ii−ii−33−33000000000000
χ876-66-66-6-300-3333i3−3i33i3−3i30-333i3−3i300000000000000000000000000000000000000−2i2i00−2i2i0000000000i−ii−i3−33−3000000000000
χ886-66-6-66-300-333−3i33i3−3i33i303-33i3−3i3000000000000000000000000000000000000002i−2i00−2i2i0000000000−iii−i3−3−33000000000000
χ896-66-6-66-300-333−3i33i3−3i33i303-33i3−3i300000000000000000000000000000000000000−2i2i002i−2i0000000000i−i−ii−333−3000000000000
χ906-66-6-66-300-3333i3−3i33i3−3i303-3−3i33i3000000000000000000000000000000000000002i−2i00−2i2i0000000000−iii−i−333−3000000000000
χ916-66-6-66-300-3333i3−3i33i3−3i303-3−3i33i300000000000000000000000000000000000000−2i2i002i−2i0000000000i−i−ii3−3−33000000000000
χ921212-12-1200-60066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-1200-60066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-612i−12i6-66−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-6−12i12i6-666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000

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