Finite Group Databasebeta

← Group #13135716

Character table — Group #13135716

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222222333344444446666666666666666666666888888121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order122344688121233666812242424243336666612121212121212121212242424242466121266612121224242424242424242424242424246666666612121212121212121616161648484848484848484412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i321−1−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+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ611111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i321−1−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+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i32
χ711111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ811111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ911111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i321−1+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−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ1011111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i321−1+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−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321−i321+i321+i32
χ1111111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ1211111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311-11-111-1-1-1-11111-11111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-11111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−ii−ii−ii−i
χ1411-11-111-1-1-1-11111-11111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-11111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ii−ii−ii
χ1511-11-111-1-1-1-11111-11111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-11111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−iii−i−i−ii−ii−ii
χ1611-11-111-1-1-1-11111-11111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-11111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii−i−iiii−ii−ii−i
χ1711-11-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11111-1-11−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i321-111-1-1-11+i321−i321−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14i−iζ22−ζ22ζ14−ζ14
χ1811-11-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11111-1-11−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i321-111-1-1-11+i321−i321−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−ii−ζ22ζ22−ζ14ζ14
χ1911-11-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11111-1-11−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32-11-1-111-11+i321−i321−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14−ii−ζ22ζ22−ζ14ζ14
χ2011-11-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11111-1-11−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32-11-1-111-11+i321−i321−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14i−iζ22−ζ22ζ14−ζ14
χ2111-11-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11111-1-11−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i321-111-1-1-11−i321+i321−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22i−iζ14−ζ14ζ22−ζ22
χ2211-11-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11111-1-11−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i321-111-1-1-11−i321+i321−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−ii−ζ14ζ14−ζ22ζ22
χ2311-11-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11111-1-11−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32-11-1-111-11−i321+i321−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22−ii−ζ14ζ14−ζ22ζ22
χ2411-11-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11111-1-11−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32-11-1-111-11−i321+i321−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22i−iζ14−ζ14ζ22−ζ22
χ252222222222222222222222-1-1-1-1-1-12222-1-1-1-1-1-1222222222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000
χ262222222222222222222222-1-1-1-1-1-12222-1-1-1-1-1-1222222-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111-2-2111111000000000000000000
χ2722222222222−1−i3−1+i3−1−i3−1+i32222222-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3222222-11+i321−i32-11+i321−i32−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000000000
χ2822222222222−1−i3−1+i3−1−i3−1+i32222222-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-2-2-2-2-2-11+i321−i32-11+i321−i32−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000000000
χ2922222222222−1+i3−1−i3−1+i3−1−i32222222-11−i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3222222-11−i321+i32-11−i321+i32−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000000000
χ3022222222222−1+i3−1−i3−1+i3−1−i32222222-11−i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-2-2-2-2-2-11−i321+i32-11−i321+i32−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000000000
χ312222222-2-22222222-22-2-2-2-2222222222222222222-2-2-2-2000000222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ322222222-2-22222222-22-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-122-2-2-2-2000000-1-1-1-1-1-1-2-211111111111100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000
χ332222222-2-22222222-22-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-122-2-2-2-2000000-1-1-1-1-1-1-2-211111111111100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000
χ342222222-2-222−1−i3−1+i3−1−i3−1+i32-22-2-2-2-22−1−i3−1+i32−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3−1−i3−1+i31+i31+i31−i31−i30000002−1−i3−1+i32−1−i3−1+i31+i31−i3-2-2-2-21+i31+i31+i31+i31−i31−i31−i31−i30000000000000000000000000000000000
χ352222222-2-222−1−i3−1+i3−1−i3−1+i32-22-2-2-2-2-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i31+i31+i31−i31−i3000000-11+i321−i32-11+i321−i321+i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200−i3i3−3+i323−i323+i32−3−i3200−i3i3−3+i323−i323+i32−3−i32000000000000000000
χ362222222-2-222−1−i3−1+i3−1−i3−1+i32-22-2-2-2-2-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i31+i31+i31−i31−i3000000-11+i321−i32-11+i321−i321+i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200i3−i33−i32−3+i32−3−i323+i3200i3−i33−i32−3+i32−3−i323+i32000000000000000000
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χ904-40400-42i2−2i200−2+2i3−2−2i32−2i32+2i3000002i2−2i2-21−i31+i32−1+i3−1−i30000−23232ζ14+4ζ22−2ζ14−4ζ22−4ζ14−2ζ224ζ14+2ζ2200−2ζ5−2ζ232ζ5+2ζ23−2ζ7−2ζ132ζ7+2ζ1300000000000000i6−i6−i2i2ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23ζ5+ζ23−ζ5−ζ23−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23ζ7+ζ13−ζ7−ζ130000000000000000000000000000000000
χ91666-366-366-3-30000-36-3-3-3-3-3000000000000000000000066-3-3-3-3000000000000000000000000000000000000000000000000000000
χ92666-366-366-3-30000-36-3-3-3-3-30000000000000000000000-6-63333000000000000000000000000000000000000000000000000000000
χ93666-366-3-6-6-3-30000-3-6-33333000000000000000000000000−3i33i3−3i33i3000000000000000000000000000000000000000000000000000000
χ94666-366-3-6-6-3-30000-3-6-333330000000000000000000000003i3−3i33i3−3i3000000000000000000000000000000000000000000000000000000
χ9566-6-3-66-3663300003-6-333-3-3000000000000000000000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000
χ9666-6-3-66-3663300003-6-333-3-30000000000000000000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000
χ9766-6-3-66-3-6-633000036-3-3-33300000000000000000000006-6-3-333000000000000000000000000000000000000000000000000000000
χ9866-6-3-66-3-6-633000036-3-3-3330000000000000000000000-6633-3-3000000000000000000000000000000000000000000000000000000
χ99121212-6-12-12-600660000-60600000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1001212-12-612-12-600-6-6000060600000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10112-120-6006−6i26i263−6300000003i6−3i63i2−3i20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-120-6006−6i26i2−63630000000−3i63i63i2−3i20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-120-60066i2−6i263−630000000−3i63i6−3i23i20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-120-60066i2−6i2−636300000003i6−3i6−3i23i20000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.