Finite Group Databasebeta

← Group #11722414

Character table — Group #11722414

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43
size1122222666666121212121212121212121212181824242424242424242424545472727272
order123461212249183636336661218181836363622991212181836363636446666
χ11111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11111111111-1-1-1-1-1-1
χ31111111111111−1−i32−1+i321−1−i32−1+i32111111111−1−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+i321−1−i32−1+i321111111-1-1−1−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−i321−1+i32−1−i32111111111−1+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−i321−1+i32−1−i321111111-1-1−1+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
χ7111-11-1-1-1111-1-111-1111-1-1-11111-111-1-111-1-1-1-11-11-11-1
χ8111-11-1-1-1111-1-111-1111-1-1-1111-1111-1-111-1-1-1-1-11-11-11
χ9111-11-1-1-1111-1-1−1−i32−1+i32-1−1−i32−1+i321-1-1-11111-1−1−i32−1+i321+i321−i32−1−i32−1+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−i32−1+i321-1-1-1111-11−1−i32−1+i321+i321−i32−1−i32−1+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+i32−1−i321-1-1-11111-1−1+i32−1−i321−i321+i32−1+i32−1−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+i32−1−i321-1-1-1111-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ13222222222-1-1-1-1222222-1-1-1-1-1-100-1-122-1-1-1-1-1-1000000
χ14222222222-1-1-1-1−1−i3−1+i32−1−i3−1+i32-1-1-1-1-1-1001+i321−i32−1−i3−1+i31+i321−i321+i321+i321−i321−i32000000
χ15222222222-1-1-1-1−1+i3−1−i32−1+i3−1−i32-1-1-1-1-1-1001−i321+i32−1+i3−1−i31−i321+i321−i321−i321+i321+i32000000
χ16222-22-2-2-22-1-11122-2222111-1-1-100-1-1-2-2-1-11111000000
χ17222-22-2-2-22-1-111−1−i3−1+i3-2−1−i3−1+i32111-1-1-1001+i321−i321+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i32000000
χ18222-22-2-2-22-1-111−1+i3−1−i3-2−1+i3−1−i32111-1-1-1001−i321+i321−i31+i31−i321+i32−1+i32−1+i32−1−i32−1−i32000000
χ193333333-1-1333300-100-1-1-1-1-1-1-1330000000000-1-10000
χ203333333-1-1333300-100-1-1-1-1-1-1-1-3-30000000000110000
χ21333-33-3-31-133-3-300100-1111-1-1-13-30000000000-110000
χ22333-33-3-31-133-3-300100-1111-1-1-1-3300000000001-10000
χ234-440-400004-400-2-2022000000000-2-200220000000000
χ244-440-400004-4001+i31−i30−1−i3−1+i30000000001+i31−i300−1−i3−1+i30000000000
χ254-440-400004-4001−i31+i30−1+i3−1−i30000000001−i31+i300−1+i3−1−i30000000000
χ264-440-40000-2223−23-2-20220000000001100-1-13−33−3000000
χ274-440-40000-2223−231+i31−i30−1−i3−1+i3000000000−1−i32−1+i32001+i321−i32−2ζ3−ζ152ζ3+ζ15ζ3+2ζ15−ζ3−2ζ15000000
χ284-440-40000-2223−231−i31+i30−1+i3−1−i3000000000−1+i32−1−i32001−i321+i32ζ3+2ζ15−ζ3−2ζ15−2ζ3−ζ152ζ3+ζ15000000
χ294-440-40000-22−2323-2-20220000000001100-1-1−33−33000000
χ304-440-40000-22−23231+i31−i30−1−i3−1+i3000000000−1−i32−1+i32001+i321−i322ζ3+ζ15−2ζ3−ζ15−ζ3−2ζ15ζ3+2ζ15000000
χ314-440-40000-22−23231−i31+i30−1+i3−1−i3000000000−1+i32−1−i32001−i321+i32−ζ3−2ζ15ζ3+2ζ152ζ3+ζ15−2ζ3−ζ15000000
χ326666666-2-2-3-3-3-300-200-2111111000000000000000000
χ33666-66-6-62-2-3-33300200-2-1-1-1111000000000000000000
χ3466-36-3-3-366000000-300-3000000000000000000000000
χ3566-36-3-3-3-2-200000010012ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34000000000000000000
χ3666-36-3-3-3-2-20000001001−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34000000000000000000
χ3766-36-3-3-3-2-200000010012ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000000000000000000
χ3866-3-6-3332-2000000-1001−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34000000000000000000
χ3966-3-6-3332-2000000-1001−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000000000000000000
χ4066-3-6-3332-2000000-10012ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34000000000000000000
χ4166-3-6-333-66000000300-3000000000000000000000000
χ4212-12-60663−63000000000000000000000000000000000000
χ4312-12-606−6363000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.