Finite Group Databasebeta

← Group #13164632

Character table — Group #13164632

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222222666666666666121212121212121212121212121212121212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order124423466612121212223446661212121233666666666612121212121212121212121222443366666666121212121212121212122244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i3211111111−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321111−1−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+i3211111111−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i32-1-1-1-1−1−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−i3211111111−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321111−1+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−i3211111111−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i32-1-1-1-1−1+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
χ71111-11-1-1-1111-1-11-111-1-1-1111-1-1111-1111-1-1-1111-1111-1-1-111111-11-111-1-1-1-1-1-111-1-111-1-111-1-11-11-11-11-11-11-1
χ81111-11-1-1-1111-1-11-111-1-1-1111-1-1111-1111-1-1-1111-1111-1-1-11111-11-1111-1-1-1-1-1-111-1-111-1-111-1-1-11-11-11-11-11-11
χ91111-11-1-1-1111-1-11-111-1-1-1111-1-1−1−i32−1+i321-1111-1-1-1−1−i32−1+i321-1111-1-1-1−1−i32−1−i32−1+i32−1+i321-11-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ101111-11-1-1-1111-1-11-111-1-1-1111-1-1−1−i32−1+i321-1111-1-1-1−1−i32−1+i321-1111-1-1-1−1−i32−1−i32−1+i32−1+i32-11-11−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ111111-11-1-1-1111-1-11-111-1-1-1111-1-1−1+i32−1−i321-1111-1-1-1−1+i32−1−i321-1111-1-1-1−1+i32−1+i32−1−i32−1−i321-11-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ121111-11-1-1-1111-1-11-111-1-1-1111-1-1−1+i32−1−i321-1111-1-1-1−1+i32−1−i321-1111-1-1-1−1+i32−1+i32−1−i32−1−i32-11-11−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-1-111-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-11-11-1-11-11
χ1411-1-111-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-11-111-11-1
χ1511-1-111-1111-1-1-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1+i32111111111+i321+i321−i321−i321-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-111-1−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ1611-1-111-1111-1-1-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1+i32111111111+i321+i321−i321−i32-111-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i321-1-111+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ1711-1-111-1111-1-1-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1−i32111111111−i321−i321+i321+i321-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-111-1−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ1811-1-111-1111-1-1-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1−i32111111111−i321−i321+i321+i32-111-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i321-1-111−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-1-111-1-11-1-111-1111-1-1-11-1-11111-11-1-1-1111111-1111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-1-1111111-1-1-1-1
χ2011-1-1-111-1-11-1-111-1111-1-1-11-1-11111-11-1-1-1111111-1111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111
χ2111-1-1-111-1-11-1-111-1111-1-1-11-1-111−1−i32−1+i32-11-1-1-1111−1−i32−1+i321-1111-1-1-11+i321+i321−i321−i3211-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ2211-1-1-111-1-11-1-111-1111-1-1-11-1-111−1−i32−1+i32-11-1-1-1111−1−i32−1+i321-1111-1-1-11+i321+i321−i321−i32-1-111−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ2311-1-1-111-1-11-1-111-1111-1-1-11-1-111−1+i32−1−i32-11-1-1-1111−1+i32−1−i321-1111-1-1-11−i321−i321+i321+i3211-1-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ2411-1-1-111-1-11-1-111-1111-1-1-11-1-111−1+i32−1−i32-11-1-1-1111−1+i32−1−i321-1111-1-1-11−i321−i321+i321+i32-1-111−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ252222222222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-122220000-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ262222222222222222-122-1-1-1-1-1-1-1−1−i3−1+i322-1-1-1-1-1-1−1−i3−1+i322-1-1-1-1-1-1−1−i3−1−i3−1+i3−1+i300001+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i32−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ272222222222222222-122-1-1-1-1-1-1-1−1+i3−1−i322-1-1-1-1-1-1−1+i3−1−i322-1-1-1-1-1-1−1+i3−1+i3−1−i3−1−i300001−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i32−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ282222-22-2-2-2222-2-22-2-12-211-1-1-111222-2-1-1-1111222-2-1-1-111122220000-1-1-2-21111-1-1-2-2-1-111-1-111000000000000
χ292222-22-2-2-2222-2-22-2-12-211-1-1-111−1−i3−1+i32-2-1-1-1111−1−i3−1+i32-2-1-1-1111−1−i3−1−i3−1+i3−1+i300001+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321+i321−i321+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000
χ302222-22-2-2-2222-2-22-2-12-211-1-1-111−1+i3−1−i32-2-1-1-1111−1+i3−1−i32-2-1-1-1111−1+i3−1+i3−1−i3−1−i300001−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i321+i321−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000
χ3122-2-222-2222-2-2-2-2-2-2-122-1-1-1111122-2-21111112222-1-1-1-1-1-1-2-2-2-20000-1-122-1-1-1-1-1-1-2-211111111000000000000
χ3222-2-222-2222-2-2-2-2-2-2-122-1-1-11111−1−i3−1+i3-2-2111111−1−i3−1+i322-1-1-1-1-1-11+i31+i31−i31−i300001+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i321+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3322-2-222-2222-2-2-2-2-2-2-122-1-1-11111−1+i3−1−i3-2-2111111−1+i3−1−i322-1-1-1-1-1-11−i31−i31+i31+i300001−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i321−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3422-2-2-222-2-22-2-222-22-12-211-111-1-122-22111-1-1-1222-2-1-1-1111-2-2-2-20000-1-1-2-21111-1-12211-1-111-1-1000000000000
χ3522-2-2-222-2-22-2-222-22-12-211-111-1-1−1−i3−1+i3-22111-1-1-1−1−i3−1+i32-2-1-1-11111+i31+i31−i31−i300001+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000
χ3622-2-2-222-2-22-2-222-22-12-211-111-1-1−1+i3−1−i3-22111-1-1-1−1+i3−1−i32-2-1-1-11111−i31−i31+i31+i300001−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000
χ3733333333333333-1-13-1-1333333300-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-10000333300000000000000000000-1-1-1-100000000
χ3833333333333333-1-13-1-1333333300-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-10000-3-3-3-300000000000000000000111100000000
χ393333-33-3-3-3333-3-3-113-11-3-3333-3-300-11-1-1-111100-11-1-1-111100003-33-300000000000000000000-11-1100000000
χ403333-33-3-3-3333-3-3-113-11-3-3333-3-300-11-1-1-111100-11-1-1-11110000-33-33000000000000000000001-11-100000000
χ4133-3-333-3333-3-3-3-3113-1-1333-3-3-3-3001111111100-1-1-1-1-1-1-1-100003-3-33000000000000000000001-1-1100000000
χ4233-3-333-3333-3-3-3-3113-1-1333-3-3-3-3001111111100-1-1-1-1-1-1-1-10000-333-300000000000000000000-111-100000000
χ4333-3-3-333-3-33-3-3331-13-11-3-33-3-333001-1111-1-1-100-11-1-1-1111000033-3-30000000000000000000011-1-100000000
χ4433-3-3-333-3-33-3-3331-13-11-3-33-3-333001-1111-1-1-100-11-1-1-11110000-3-33300000000000000000000-1-11100000000
χ454-44i−4i04000-44i−4i000040000-44i−4i00-2-20000000022000000002i−2i2i−2i0000-2-200000022002i−2i002i−2i00000000000000
χ464-44i−4i04000-44i−4i000040000-44i−4i001+i31−i300000000−1−i3−1+i3000000002ζ11−2ζ112ζ7−2ζ700001+i31−i3000000−1−i3−1+i3002ζ11−2ζ11002ζ7−2ζ700000000000000
χ474-44i−4i04000-44i−4i000040000-44i−4i001−i31+i300000000−1+i3−1−i3000000002ζ7−2ζ72ζ11−2ζ1100001−i31+i3000000−1+i3−1−i3002ζ7−2ζ7002ζ11−2ζ1100000000000000
χ484-44i−4i04000-44i−4i0000-200−2i32i32−2i2i23−23-2-20000000022000000002i−2i2i−2i00001100−i3i3−i3i3-1-100−ii3−3−ii3−3000000000000
χ494-44i−4i04000-44i−4i0000-200−2i32i32−2i2i23−231+i31−i300000000−1−i3−1+i3000000002ζ11−2ζ112ζ7−2ζ70000−1−i32−1+i3200−3+i323−i323+i32−3−i321+i321−i3200−ζ11ζ112ζ7+ζ11−2ζ7−ζ11−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11000000000000
χ504-44i−4i04000-44i−4i0000-200−2i32i32−2i2i23−231−i31+i300000000−1+i3−1−i3000000002ζ7−2ζ72ζ11−2ζ110000−1+i32−1−i32003+i32−3−i32−3+i323−i321−i321+i3200−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11−ζ11ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ514-44i−4i04000-44i−4i0000-2002i3−2i32−2i2i−2323-2-20000000022000000002i−2i2i−2i00001100i3−i3i3−i3-1-100−ii−33−ii−33000000000000
χ524-44i−4i04000-44i−4i0000-2002i3−2i32−2i2i−23231+i31−i300000000−1−i3−1+i3000000002ζ11−2ζ112ζ7−2ζ70000−1−i32−1+i32003−i32−3+i32−3−i323+i321+i321−i3200−ζ11ζ11−2ζ7−ζ112ζ7+ζ11−ζ7ζ7ζ7+2ζ11−ζ7−2ζ11000000000000
χ534-44i−4i04000-44i−4i0000-2002i3−2i32−2i2i−23231−i31+i300000000−1+i3−1−i3000000002ζ7−2ζ72ζ11−2ζ110000−1+i32−1−i3200−3−i323+i323−i32−3+i321−i321+i3200−ζ7ζ7ζ7+2ζ11−ζ7−2ζ11−ζ11ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ544-4−4i4i04000-4−4i4i000040000-4−4i4i00-2-2000000002200000000−2i2i−2i2i0000-2-20000002200−2i2i00−2i2i00000000000000
χ554-4−4i4i04000-4−4i4i000040000-4−4i4i001+i31−i300000000−1−i3−1+i300000000−2ζ112ζ11−2ζ72ζ700001+i31−i3000000−1−i3−1+i300−2ζ112ζ1100−2ζ72ζ700000000000000
χ564-4−4i4i04000-4−4i4i000040000-4−4i4i001−i31+i300000000−1+i3−1−i300000000−2ζ72ζ7−2ζ112ζ1100001−i31+i3000000−1+i3−1−i300−2ζ72ζ700−2ζ112ζ1100000000000000
χ574-4−4i4i04000-4−4i4i0000-200−2i32i322i−2i−2323-2-2000000002200000000−2i2i−2i2i00001100−i3i3−i3i3-1-100i−i−33i−i−33000000000000
χ584-4−4i4i04000-4−4i4i0000-200−2i32i322i−2i−23231+i31−i300000000−1−i3−1+i300000000−2ζ112ζ11−2ζ72ζ70000−1−i32−1+i3200−3+i323−i323+i32−3−i321+i321−i3200ζ11−ζ11−2ζ7−ζ112ζ7+ζ11ζ7−ζ7ζ7+2ζ11−ζ7−2ζ11000000000000
χ594-4−4i4i04000-4−4i4i0000-200−2i32i322i−2i−23231−i31+i300000000−1+i3−1−i300000000−2ζ72ζ7−2ζ112ζ110000−1+i32−1−i32003+i32−3−i32−3+i323−i321−i321+i3200ζ7−ζ7ζ7+2ζ11−ζ7−2ζ11ζ11−ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ604-4−4i4i04000-4−4i4i0000-2002i3−2i322i−2i23−23-2-2000000002200000000−2i2i−2i2i00001100i3−i3i3−i3-1-100i−i3−3i−i3−3000000000000
χ614-4−4i4i04000-4−4i4i0000-2002i3−2i322i−2i23−231+i31−i300000000−1−i3−1+i300000000−2ζ112ζ11−2ζ72ζ70000−1−i32−1+i32003−i32−3+i32−3−i323+i321+i321−i3200ζ11−ζ112ζ7+ζ11−2ζ7−ζ11ζ7−ζ7−ζ7−2ζ11ζ7+2ζ11000000000000
χ624-4−4i4i04000-4−4i4i0000-2002i3−2i322i−2i23−231−i31+i300000000−1+i3−1−i300000000−2ζ72ζ7−2ζ112ζ110000−1+i32−1−i3200−3−i323+i323−i32−3+i321−i321+i3200ζ7−ζ7−ζ7−2ζ11ζ7+2ζ11ζ11−ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ6366666666666666-2-2-3-2-2-3-3-3-3-3-3-300-2-211111100-2-21111110000000000000000000000000000000000000000
χ6466666-36-3-3-3-3-3-3-366066000000000-3-300000000-3-30000000000000000000000000000000000000000000000
χ6566666-36-3-3-3-3-3-3-3-2-20-2-2000000000114-2-24-2-200114-2-24-2-20000000000000000000000000000000000000000
χ6666666-36-3-3-3-3-3-3-3-2-20-2-200000000011-24-2-24-20011-24-2-24-20000000000000000000000000000000000000000
χ6766666-36-3-3-3-3-3-3-3-2-20-2-200000000011-2-24-2-240011-2-24-2-240000000000000000000000000000000000000000
χ686666-66-6-6-6666-6-6-22-3-2233-3-3-33300-22111-1-1-100-22111-1-1-10000000000000000000000000000000000000000
χ696666-6-3-633-3-3-3336-606-6000000000-3300000000-330000000000000000000000000000000000000000000000
χ706666-6-3-633-3-3-333-220-220000000001-14-2-2-422001-14-2-2-4220000000000000000000000000000000000000000
χ716666-6-3-633-3-3-333-220-220000000001-1-24-22-42001-1-24-22-420000000000000000000000000000000000000000
χ726666-6-3-633-3-3-333-220-220000000001-1-2-2422-4001-1-2-2422-40000000000000000000000000000000000000000
χ7366-6-666-6666-6-6-6-622-3-2-2-3-3-333330022-1-1-1-1-1-100-2-21111110000000000000000000000000000000000000000
χ7466-6-66-3-6-3-3-33333220-2-2000000000-1-122-422-40011-2-24-2-240000000000000000000000000000000000000000
χ7566-6-66-3-6-3-3-33333220-2-2000000000-1-12-422-420011-24-2-24-20000000000000000000000000000000000000000
χ7666-6-66-3-6-3-3-33333220-2-2000000000-1-1-422-42200114-2-24-2-20000000000000000000000000000000000000000
χ7766-6-66-3-6-3-3-33333-6-60660000000003300000000-3-30000000000000000000000000000000000000000000000
χ7866-6-6-666-6-66-6-6662-2-3-2233-333-3-3002-2-1-1-111100-22111-1-1-10000000000000000000000000000000000000000
χ7966-6-6-6-3633-333-3-32-20-22000000000-1122-4-2-24001-1-2-2422-40000000000000000000000000000000000000000
χ8066-6-6-6-3633-333-3-32-20-22000000000-112-42-24-2001-1-24-22-420000000000000000000000000000000000000000
χ8166-6-6-6-3633-333-3-32-20-22000000000-11-4224-2-2001-14-2-2-4220000000000000000000000000000000000000000
χ8266-6-6-6-3633-333-3-3-6606-60000000003-300000000-330000000000000000000000000000000000000000000000
χ8312-1212i−12i0-60−6i36i36−6i6i63−63000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212i−12i0-606i3−6i36−6i6i−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12−12i12i0-60−6i36i366i−6i−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12−12i12i0-606i3−6i366i−6i63−63000000000000000000000000000000000000000000000000000000000000000000000000

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