Finite Group Databasebeta

← Group #13147218

Character table — Group #13147218

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222222666666666666121212121212121212121212121212121212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order122234466612121212344446661212121233666666121212121212121212121212121212122244336666661212121212121212121212124444666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ611111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ711111-1-1111-1-1-1-11-1-111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ811111-1-1111-1-1-1-11-1-111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ911111-1-1111-1-1-1-11-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1011111-1-1111-1-1-1-11-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1111111-1-1111-1-1-1-11-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1211111-1-1111-1-1-1-11-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ131-1-111i−i-11-1ii−i−i1i−i1-1-11-1ii−i−i1111-1-1-1-11-1i−i111-1-1-1iii−i−i−i1-1i−i111-11-1-1-1i−ii−iii−i−iii−i−ii−i1-11-11-1i−ii−i
χ141-1-111i−i-11-1ii−i−i1i−i1-1-11-1ii−i−i1111-1-1-1-11-1i−i111-1-1-1iii−i−i−i-11−ii111-11-1-1-1i−ii−iii−i−iii−i−i−ii-11-11-11−ii−ii
χ151-1-111i−i-11-1ii−i−i1i−i1-1-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1i−i111-1-1-1iii−i−i−i1-1i−i−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7i−i1-1−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ7
χ161-1-111i−i-11-1ii−i−i1i−i1-1-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1i−i111-1-1-1iii−i−i−i-11−ii−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−ii-111+i32−1−i321−i32−1+i32−ζ11ζ11−ζ7ζ7
χ171-1-111i−i-11-1ii−i−i1i−i1-1-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1i−i111-1-1-1iii−i−i−i1-1i−i−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11i−i1-1−1+i321−i32−1−i321+i32ζ7−ζ7ζ11−ζ11
χ181-1-111i−i-11-1ii−i−i1i−i1-1-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1i−i111-1-1-1iii−i−i−i-11−ii−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−ii-111−i32−1+i321+i32−1−i32−ζ7ζ7−ζ11ζ11
χ191-1-111−ii-11-1−i−iii1−ii1-1-11-1−i−iii1111-1-1-1-11-1−ii111-1-1-1−i−i−iiii1-1−ii111-11-1-1-1−ii−ii−i−iii−i−iii−ii1-11-11-1−ii−ii
χ201-1-111−ii-11-1−i−iii1−ii1-1-11-1−i−iii1111-1-1-1-11-1−ii111-1-1-1−i−i−iiii-11i−i111-11-1-1-1−ii−ii−i−iii−i−iiii−i-11-11-11i−ii−i
χ211-1-111−ii-11-1−i−iii1−ii1-1-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−ii111-1-1-1−i−i−iiii1-1−ii−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ii1-1−1−i321+i32−1+i321−i32−ζ11ζ11−ζ7ζ7
χ221-1-111−ii-11-1−i−iii1−ii1-1-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−ii111-1-1-1−i−i−iiii-11i−i−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7i−i-111+i32−1−i321−i32−1+i32ζ11−ζ11ζ7−ζ7
χ231-1-111−ii-11-1−i−iii1−ii1-1-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1−ii111-1-1-1−i−i−iiii1-1−ii−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ii1-1−1+i321−i32−1−i321+i32−ζ7ζ7−ζ11ζ11
χ241-1-111−ii-11-1−i−iii1−ii1-1-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1−ii111-1-1-1−i−i−iiii-11i−i−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11i−i-111−i32−1+i321+i32−1−i32ζ7−ζ7ζ11−ζ11
χ2522222222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2622222222222222-12222-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-100001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ2722222222222222-12222-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-100001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ2822222-2-2222-2-2-2-2-1-2-222-1-1-111112222222222-2-2-1-1-1-1-1-11111110000-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2922222-2-2222-2-2-2-2-1-2-222-1-1-11111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-2-2-1-1-1-1-1-111111100001+i321−i321+i321+i321−i321−i321+i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3022222-2-2222-2-2-2-2-1-2-222-1-1-11111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-2-2-1-1-1-1-1-111111100001−i321+i321−i321−i321+i321+i321−i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ312-2-2222i−2i-22-22i2i−2i−2i-12i−2i2-21-11−i−iii2222-2-2-2-22-22i−2i-1-1-1111−i−i−iiii0000-1-1-11-11112i−2i2i−2i−i−iii−i−iii000000000000
χ322-2-2222i−2i-22-22i2i−2i−2i-12i−2i2-21-11−i−iii−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-22i−2i-1-1-1111−i−i−iiii00001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i322ζ11−2ζ112ζ7−2ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7000000000000
χ332-2-2222i−2i-22-22i2i−2i−2i-12i−2i2-21-11−i−iii−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-22i−2i-1-1-1111−i−i−iiii00001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i322ζ7−2ζ72ζ11−2ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11000000000000
χ342-2-222−2i2i-22-2−2i−2i2i2i-1−2i2i2-21-11ii−i−i2222-2-2-2-22-2−2i2i-1-1-1111iii−i−i−i0000-1-1-11-1111−2i2i−2i2iii−i−iii−i−i000000000000
χ352-2-222−2i2i-22-2−2i−2i2i2i-1−2i2i2-21-11ii−i−i−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-2−2i2i-1-1-1111iii−i−i−i00001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32−2ζ112ζ11−2ζ72ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7000000000000
χ362-2-222−2i2i-22-2−2i−2i2i2i-1−2i2i2-21-11ii−i−i−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-2−2i2i-1-1-1111iii−i−i−i00001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32−2ζ72ζ7−2ζ112ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11000000000000
χ37333333333333333-1-1-1-1333333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333300000000000000000000-1-1-1-100000000
χ38333333333333333-1-1-1-1333333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000000000000000111100000000
χ3933333-3-3333-3-3-3-3311-1-1333-3-3-3-300000000-1-111-1-1-1-1-1-111111133-3-30000000000000000000011-1-100000000
χ4033333-3-3333-3-3-3-3311-1-1333-3-3-3-300000000-1-111-1-1-1-1-1-1111111-3-33300000000000000000000-1-11100000000
χ413-3-3333i−3i-33-33i3i−3i−3i3−ii-11-33-33i3i−3i−3i00000000-11−ii-1-1-1111−i−i−iiii3-33i−3i00000000000000000000−ii-1100000000
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χ4844-4-4400-4-440000-2000022-223−2323−23-2-22222-2-20000000000000000000011-11-11-1-100003−33−33−33−3000000000000
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χ5144-4-4400-4-440000-2000022-2−2323−2323-2-22222-2-20000000000000000000011-11-11-1-10000−33−33−33−33000000000000
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χ5344-4-4400-4-440000-2000022-2−2323−23231−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000000000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i320000ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ544-44-44004-4-40000400004-4-40000-2-222-2-22200000000000000000000-2-22222-2-2000000000000000000000000
χ554-44-44004-4-40000400004-4-400001+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3000000000000000000001+i31−i3−1−i3−1−i3−1+i3−1+i31+i31−i3000000000000000000000000
χ564-44-44004-4-40000400004-4-400001−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3000000000000000000001−i31+i3−1+i3−1+i3−1−i3−1−i31−i31+i3000000000000000000000000
χ574-44-44004-4-40000-20000-222−2i32i32i3−2i3-2-222-2-2220000000000000000000011-1-1-1-1110000−i3i3i3−i3−i3i3i3−i3000000000000
χ584-44-44004-4-40000-20000-222−2i32i32i3−2i31+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i300000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i320000−3+i323−i323−i32−3+i323+i32−3−i32−3−i323+i32000000000000
χ594-44-44004-4-40000-20000-222−2i32i32i3−2i31−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i300000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200003+i32−3−i32−3−i323+i32−3+i323−i323−i32−3+i32000000000000
χ604-44-44004-4-40000-20000-2222i3−2i3−2i32i3-2-222-2-2220000000000000000000011-1-1-1-1110000i3−i3−i3i3i3−i3−i3i3000000000000
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χ6366666666666666-3-2-2-2-2-3-3-3-3-3-3-300000000-2-2-2-2111111111111000000000000000000000000000000000000
χ6466666-6-6666-6-6-6-6-322-2-2-3-3-3333300000000-2-222111111-1-1-1-1-1-1000000000000000000000000000000000000
χ656666-366-3-3-3-3-3-3-306666000000000000000-3-3-3-3000000000000000000000000000000000000000000000000
χ666666-366-3-3-3-3-3-3-30-2-2-2-200000000000000011114-2-24-2-24-2-24-2-2000000000000000000000000000000000000
χ676666-366-3-3-3-3-3-3-30-2-2-2-20000000000000001111-24-2-24-2-24-2-24-2000000000000000000000000000000000000
χ686666-366-3-3-3-3-3-3-30-2-2-2-20000000000000001111-2-24-2-24-2-24-2-24000000000000000000000000000000000000
χ696666-3-6-6-3-3-33333022-2-200000000000000011-1-14-2-24-2-2-422-422000000000000000000000000000000000000
χ706666-3-6-6-3-3-33333022-2-200000000000000011-1-1-24-2-24-22-422-42000000000000000000000000000000000000
χ716666-3-6-6-3-3-33333022-2-200000000000000011-1-1-2-24-2-2422-422-4000000000000000000000000000000000000
χ726666-3-6-6-3-3-333330-6-666000000000000000-3-333000000000000000000000000000000000000000000000000
χ736-6-6666i−6i-66-66i6i−6i−6i-3−2i2i-223-33−3i−3i3i3i00000000-22−2i2i111-1-1-1iii−i−i−i000000000000000000000000000000000000
χ746-6-666−6i6i-66-6−6i−6i6i6i-32i−2i-223-333i3i−3i−3i00000000-222i−2i111-1-1-1−i−i−iiii000000000000000000000000000000000000
χ756-6-66-36i−6i3-33−3i−3i3i3i06i−6i6-6000000000000000-33−3i3i000000000000000000000000000000000000000000000000
χ766-6-66-36i−6i3-33−3i−3i3i3i0−2i2i-220000000000000001-1i−i4-2-2-4224i−2i−2i−4i2i2i000000000000000000000000000000000000
χ776-6-66-36i−6i3-33−3i−3i3i3i0−2i2i-220000000000000001-1i−i-24-22-42−2i4i−2i2i−4i2i000000000000000000000000000000000000
χ786-6-66-36i−6i3-33−3i−3i3i3i0−2i2i-220000000000000001-1i−i-2-2422-4−2i−2i4i2i2i−4i000000000000000000000000000000000000
χ796-6-66-3−6i6i3-333i3i−3i−3i02i−2i-220000000000000001-1−ii4-2-2-422−4i2i2i4i−2i−2i000000000000000000000000000000000000
χ806-6-66-3−6i6i3-333i3i−3i−3i02i−2i-220000000000000001-1−ii-24-22-422i−4i2i−2i4i−2i000000000000000000000000000000000000
χ816-6-66-3−6i6i3-333i3i−3i−3i02i−2i-220000000000000001-1−ii-2-2422-42i2i−4i−2i−2i4i000000000000000000000000000000000000
χ826-6-66-3−6i6i3-333i3i−3i−3i0−6i6i6-6000000000000000-333i−3i000000000000000000000000000000000000000000000000
χ831212-12-12-60066-663−6363−63000000000000000000000000000000000000000000000000000000000000000000000000
χ841212-12-12-60066-6−6363−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-1212-12-600-666−6i36i36i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-600-6666i3−6i3−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000

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