Finite Group Databasebeta

← Group #13164631

Character table — Group #13164631

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11222226666661212121212121212121212121818242424242424242424245454727272721122222666666121212121212121212121212181824242424242424242424545472727272
order123461212234612123366666612121212223366121212121212446666226461212264612126666666612121212226666121212121212446666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11111111111-1-1-1-1-1-11111111111111111111111111-1-11111111111-1-1-1-1-1-1
χ31111111111111−1−i32−1+i321111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111111111111−1−i32−1+i321111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ41111111111111−1−i32−1+i321111−1−i32−1+i321111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321111111111111−1−i32−1+i321111−1−i32−1+i321111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ51111111111111−1+i32−1−i321111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111111111111−1+i32−1−i321111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ61111111111111−1+i32−1−i321111−1+i32−1−i321111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321111111111111−1+i32−1−i321111−1+i32−1−i321111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ7111-11-1-1-1111-1-111-1-1-1-11111111-11111-1-1-1-1-1-11-11-11-1111-11-1-1-1111-1-111-1-1-1-11111111-11111-1-1-1-1-1-11-11-11-1
χ8111-11-1-1-1111-1-111-1-1-1-1111111-111111-1-1-1-1-1-1-11-11-11111-11-1-1-1111-1-111-1-1-1-1111111-111111-1-1-1-1-1-1-11-11-11
χ9111-11-1-1-1111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i3211111-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32111-11-1-1-1111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i3211111-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ10111-11-1-1-1111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i321111-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32111-11-1-1-1111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i321111-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32
χ11111-11-1-1-1111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i3211111-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32111-11-1-1-1111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i3211111-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ12111-11-1-1-1111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i321111-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32111-11-1-1-1111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i321111-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ1322222222-12-1-1-1222-1-1-1222-1-1-100-1-1-1-122-1-1-1-100000022222222-12-1-1-1222-1-1-1222-1-1-100-1-1-1-122-1-1-1-1000000
χ1422222222-12-1-1-1−1−i3−1+i32-1-1-1−1−i3−1+i32-1-1-1001+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i3200000022222222-12-1-1-1−1−i3−1+i32-1-1-1−1−i3−1+i32-1-1-1001+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32000000
χ1522222222-12-1-1-1−1+i3−1−i32-1-1-1−1+i3−1−i32-1-1-1001−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i3200000022222222-12-1-1-1−1+i3−1−i32-1-1-1−1+i3−1−i32-1-1-1001−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32000000
χ16222-22-2-2-2-12-11122-2111222-1-1-100-1-1-1-1-2-21111000000222-22-2-2-2-12-11122-2111222-1-1-100-1-1-1-1-2-21111000000
χ17222-22-2-2-2-12-111−1−i3−1+i3-2111−1−i3−1+i32-1-1-1001+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i32000000222-22-2-2-2-12-111−1−i3−1+i3-2111−1−i3−1+i32-1-1-1001+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i32000000
χ18222-22-2-2-2-12-111−1+i3−1−i3-2111−1+i3−1−i32-1-1-1001−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i32000000222-22-2-2-2-12-111−1+i3−1−i3-2111−1+i3−1−i32-1-1-1001−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i32000000
χ193333333-13-133300-1-1-1-100-1-1-1-1330000000000-1-100003333333-13-133300-1-1-1-100-1-1-1-1330000000000-1-10000
χ203333333-13-133300-1-1-1-100-1-1-1-1-3-300000000001100003333333-13-133300-1-1-1-100-1-1-1-1-3-30000000000110000
χ21333-33-3-313-13-3-300111100-1-1-1-13-30000000000-110000333-33-3-313-13-3-300111100-1-1-1-13-30000000000-110000
χ22333-33-3-313-13-3-300111100-1-1-1-1-3300000000001-10000333-33-3-313-13-3-300111100-1-1-1-1-3300000000001-10000
χ234-440-400040-400-2-2000022000000-2-2220000000000004-440-400040-400-2-2000022000000-2-222000000000000
χ244-440-400040-4001+i31−i30000−1−i3−1+i30000001+i31−i3−1−i3−1+i30000000000004-440-400040-4001+i31−i30000−1−i3−1+i30000001+i31−i3−1−i3−1+i3000000000000
χ254-440-400040-4001−i31+i30000−1+i3−1−i30000001−i31+i3−1+i3−1−i30000000000004-440-400040-4001−i31+i30000−1+i3−1−i30000001−i31+i3−1+i3−1−i3000000000000
χ264-440-4000-20223−23-2-200002200000011-1-1003−33−30000004-440-4000-20223−23-2-200002200000011-1-1003−33−3000000
χ274-440-4000-20223−231+i31−i30000−1−i3−1+i3000000−1−i32−1+i321+i321−i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ110000004-440-4000-20223−231+i31−i30000−1−i3−1+i3000000−1−i32−1+i321+i321−i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000
χ284-440-4000-20223−231−i31+i30000−1+i3−1−i3000000−1+i32−1−i321−i321+i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ110000004-440-4000-20223−231−i31+i30000−1+i3−1−i3000000−1+i32−1−i321−i321+i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000
χ294-440-4000-202−2323-2-200002200000011-1-100−33−330000004-440-4000-202−2323-2-200002200000011-1-100−33−33000000
χ304-440-4000-202−23231+i31−i30000−1−i3−1+i3000000−1−i32−1+i321+i321−i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ110000004-440-4000-202−23231+i31−i30000−1−i3−1+i3000000−1−i32−1+i321+i321−i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000
χ314-440-4000-202−23231−i31+i30000−1+i3−1−i3000000−1+i32−1−i321−i321+i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ110000004-440-4000-202−23231−i31+i30000−1+i3−1−i3000000−1+i32−1−i321−i321+i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000
χ326666666-2-3-2-3-3-300-211100-21110000000000000000006666666-2-3-2-3-3-300-211100-2111000000000000000000
χ33666-66-6-62-3-2-333002-1-1-100-2111000000000000000000666-66-6-62-3-2-333002-1-1-100-2111000000000000000000
χ3466-36-3-3-360600000-300000-300000000000000000000066-36-3-3-360600000-300000-3000000000000000000000
χ3566-36-3-3-3-20-20000014-2-20014-2-200000000000000000066-36-3-3-3-20-20000014-2-20014-2-2000000000000000000
χ3666-36-3-3-3-20-2000001-24-2001-24-200000000000000000066-36-3-3-3-20-2000001-24-2001-24-2000000000000000000
χ3766-36-3-3-3-20-2000001-2-24001-2-2400000000000000000066-36-3-3-3-20-2000001-2-24001-2-24000000000000000000
χ3866-3-6-33320-200000-122-4001-2-2400000000000000000066-3-6-33320-200000-122-4001-2-24000000000000000000
χ3966-3-6-33320-200000-12-42001-24-200000000000000000066-3-6-33320-200000-12-42001-24-2000000000000000000
χ4066-3-6-33320-200000-1-4220014-2-200000000000000000066-3-6-33320-200000-1-4220014-2-2000000000000000000
χ4166-3-6-333-60600000300000-300000000000000000000066-3-6-333-60600000300000-3000000000000000000000
χ4212-12-60663−6300000000000000000000000000000000000012-12-60663−63000000000000000000000000000000000000
χ4312-12-606−636300000000000000000000000000000000000012-12-606−6363000000000000000000000000000000000000
χ441111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ451111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ461111111111111−1−i32−1+i321111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i32-1-1-1-11+i321−i32-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ471111111111111−1−i32−1+i321111−1−i32−1+i321111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i32-1-1-1-11+i321−i32-1-1-1-1111+i321−i321+i321−i321+i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ481111111111111−1+i32−1−i321111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i32-1-1-1-11−i321+i32-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ491111111111111−1+i32−1−i321111−1+i32−1−i321111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i32-1-1-1-11−i321+i32-1-1-1-1111−i321+i321−i321+i321−i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ50111-11-1-1-1111-1-111-1-1-1-11111111-11111-1-1-1-1-1-11-11-11-1-1-1-11-1111-1-1-111-1-11111-1-1-1-1-1-1-11-1-1-1-1111111-11-11-11
χ51111-11-1-1-1111-1-111-1-1-1-1111111-111111-1-1-1-1-1-1-11-11-11-1-1-11-1111-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-1-11111111-11-11-1
χ52111-11-1-1-1111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i3211111-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32-1-1-11-1111-1-1-1111+i321−i3211111+i321−i32-1-1-1-1-111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ53111-11-1-1-1111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i321111-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-1-1-11-1111-1-1-1111+i321−i3211111+i321−i32-1-1-1-11-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32
χ54111-11-1-1-1111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i3211111-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32-1-1-11-1111-1-1-1111−i321+i3211111−i321+i32-1-1-1-1-111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ55111-11-1-1-1111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i321111-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-1-1-11-1111-1-1-1111−i321+i3211111−i321+i32-1-1-1-11-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32
χ5622222222-12-1-1-1222-1-1-1222-1-1-100-1-1-1-122-1-1-1-1000000-2-2-2-2-2-2-2-21-2111-2-2-2111-2-2-2111001111-2-21111000000
χ5722222222-12-1-1-1−1−i3−1+i32-1-1-1−1−i3−1+i32-1-1-1001+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32000000-2-2-2-2-2-2-2-21-21111+i31−i3-21111+i31−i3-211100−1−i32−1+i32−1−i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i32000000
χ5822222222-12-1-1-1−1+i3−1−i32-1-1-1−1+i3−1−i32-1-1-1001−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32000000-2-2-2-2-2-2-2-21-21111−i31+i3-21111−i31+i3-211100−1+i32−1−i32−1+i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i32000000
χ59222-22-2-2-2-12-11122-2111222-1-1-100-1-1-1-1-2-21111000000-2-2-22-22221-21-1-1-2-22-1-1-1-2-2-211100111122-1-1-1-1000000
χ60222-22-2-2-2-12-111−1−i3−1+i3-2111−1−i3−1+i32-1-1-1001+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i32000000-2-2-22-22221-21-1-11+i31−i32-1-1-11+i31−i3-211100−1−i32−1+i32−1−i32−1+i32−1−i3−1+i31+i321+i321−i321−i32000000
χ61222-22-2-2-2-12-111−1+i3−1−i3-2111−1+i3−1−i32-1-1-1001−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i32000000-2-2-22-22221-21-1-11−i31+i32-1-1-11−i31+i3-211100−1+i32−1−i32−1+i32−1−i32−1+i3−1−i31−i321−i321+i321+i32000000
χ623333333-13-133300-1-1-1-100-1-1-1-1330000000000-1-10000-3-3-3-3-3-3-31-31-3-3-3001111001111-3-30000000000110000
χ633333333-13-133300-1-1-1-100-1-1-1-1-3-30000000000110000-3-3-3-3-3-3-31-31-3-3-3001111001111330000000000-1-10000
χ64333-33-3-313-13-3-300111100-1-1-1-13-30000000000-110000-3-3-33-333-1-31-33300-1-1-1-1001111-3300000000001-10000
χ65333-33-3-313-13-3-300111100-1-1-1-1-3300000000001-10000-3-3-33-333-1-31-33300-1-1-1-10011113-30000000000-110000
χ664-440-400040-400-2-2000022000000-2-222000000000000-44-404000-40400220000-2-200000022-2-2000000000000
χ674-440-400040-4001+i31−i30000−1−i3−1+i30000001+i31−i3−1−i3−1+i3000000000000-44-404000-40400−1−i3−1+i300001+i31−i3000000−1−i3−1+i31+i31−i3000000000000
χ684-440-400040-4001−i31+i30000−1+i3−1−i30000001−i31+i3−1+i3−1−i3000000000000-44-404000-40400−1+i3−1−i300001−i31+i3000000−1+i3−1−i31−i31+i3000000000000
χ694-440-4000-20223−23-2-200002200000011-1-1003−33−3000000-44-40400020-2−2323220000-2-2000000-1-11100−33−33000000
χ704-440-4000-20223−231+i31−i30000−1−i3−1+i3000000−1−i32−1+i321+i321−i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000-44-40400020-2−2323−1−i3−1+i300001+i31−i30000001+i321−i32−1−i32−1+i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000
χ714-440-4000-20223−231−i31+i30000−1+i3−1−i3000000−1+i32−1−i321−i321+i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000-44-40400020-2−2323−1+i3−1−i300001−i31+i30000001−i321+i32−1+i32−1−i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000
χ724-440-4000-202−2323-2-200002200000011-1-100−33−33000000-44-40400020-223−23220000-2-2000000-1-111003−33−3000000
χ734-440-4000-202−23231+i31−i30000−1−i3−1+i3000000−1−i32−1+i321+i321−i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000-44-40400020-223−23−1−i3−1+i300001+i31−i30000001+i321−i32−1−i32−1+i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000
χ744-440-4000-202−23231−i31+i30000−1+i3−1−i3000000−1+i32−1−i321−i321+i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000-44-40400020-223−23−1+i3−1−i300001−i31+i30000001−i321+i32−1+i32−1−i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000
χ756666666-2-3-2-3-3-300-211100-2111000000000000000000-6-6-6-6-6-6-6232333002-1-1-1002-1-1-1000000000000000000
χ76666-66-6-62-3-2-333002-1-1-100-2111000000000000000000-6-6-66-666-2323-3-300-2111002-1-1-1000000000000000000
χ7766-36-3-3-360600000-300000-3000000000000000000000-6-63-6333-60-6000003000003000000000000000000000
χ7866-36-3-3-3-20-20000014-2-20014-2-2000000000000000000-6-63-633320200000-1-42200-1-422000000000000000000
χ7966-36-3-3-3-20-2000001-24-2001-24-2000000000000000000-6-63-633320200000-12-4200-12-42000000000000000000
χ8066-36-3-3-3-20-2000001-2-24001-2-24000000000000000000-6-63-633320200000-122-400-122-4000000000000000000
χ8166-3-6-33320-200000-122-4001-2-24000000000000000000-6-6363-3-3-202000001-2-2400-122-4000000000000000000
χ8266-3-6-33320-200000-12-42001-24-2000000000000000000-6-6363-3-3-202000001-24-200-12-42000000000000000000
χ8366-3-6-33320-200000-1-4220014-2-2000000000000000000-6-6363-3-3-2020000014-2-200-1-422000000000000000000
χ8466-3-6-333-60600000300000-3000000000000000000000-6-6363-3-360-600000-3000003000000000000000000000
χ8512-12-60663−63000000000000000000000000000000000000-121260-6−6363000000000000000000000000000000000000
χ8612-12-606−6363000000000000000000000000000000000000-121260-663−63000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.