Finite Group Databasebeta

← Group #13135619

Character table — Group #13135619

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11222223333444444444446666666666666688888121212121212121212121212121212121212121212121212121212122424242424242424242424242424727272727272727272727272
order1223666336644444121212121212669991818181818181818182661212121212121212121212123636363636363636363636363636363636366618181818181836363636363688882424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-111111111111111111111-1-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i
χ411111111111111-1-111111111111111111111-1-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii
χ5111111111111-1-111-1-1-1-11111111111111111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111-11-111-1-111-1-1
χ6111111111111-1-111-1-1-1-11111111111111111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-11-11-1-111-1-111
χ7111111111111-1-1-1-1-1-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1i−i−iiii−i−i−i−iii
χ8111111111111-1-1-1-1-1-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1−iii−i−i−iiiii−i−i
χ91111111−1−i32−1+i32−1−i32−1+i3211111111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211111−1−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+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i32
χ101111111−1−i32−1+i32−1−i32−1+i3211111111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211111−1−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+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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
χ111111111−1−i32−1+i32−1−i32−1+i32111-1-1111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32ii−i−iζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ121111111−1−i32−1+i32−1−i32−1+i32111-1-1111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32−i−iii−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ131111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ141111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ151111111−1−i32−1+i32−1−i32−1+i321-1-1-1-1-1-1-1-111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32i−i−iiζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ161111111−1−i32−1+i32−1−i32−1+i321-1-1-1-1-1-1-1-111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32−iii−i−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ171111111−1+i32−1−i32−1+i32−1−i3211111111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211111−1+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−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+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−i32
χ181111111−1+i32−1−i32−1+i32−1−i3211111111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211111−1+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−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+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
χ191111111−1+i32−1−i32−1+i32−1−i32111-1-1111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32ii−i−iζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11
χ201111111−1+i32−1−i32−1+i32−1−i32111-1-1111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32−i−iii−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11
χ211111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ221111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ231111111−1+i32−1−i32−1+i32−1−i321-1-1-1-1-1-1-1-111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32i−i−iiζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11
χ241111111−1+i32−1−i32−1+i32−1−i321-1-1-1-1-1-1-1-111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32−iii−i−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11
χ25222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2622222222222222-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111111111000000000000
χ27222222222222-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-22222-2-2-2-22222111111111111-1-1-1-1-1-1-2-2111111-1-1-1-1-1-1000000000000
χ28222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1222-2-222-2-2-2-2-2-2-2-2111111111111-1-1-1-1-1-122-1-1-1-1-1-1111111000000000000
χ2922222222222-2002-20000-2-2222222222222220002-2-2-200002-22-2000000000000-2-2-2-2-2-2000000002-22-22-2000000000000
χ3022222222222-2002-20000-2-222-1-1-1-1-1-1-1-1-1-1-1-10002-2-2-200002-22-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311111100−i3i3−i3i3−i3i3-11-11-11000000000000
χ3122222222222-2002-20000-2-222-1-1-1-1-1-1-1-1-1-1-1-10002-2-2-200002-22-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311111100i3−i3i3−i3i3−i3-11-11-11000000000000
χ3222222222222-200-220000-2-222222222222222000-22-2-20000-22-22000000000000-2-2-2-2-2-200000000-22-22-22000000000000
χ3322222222222-200-220000-2-222-1-1-1-1-1-1-1-1-1-1-1-1000-22-2-20000-22-22−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311111100i3−i3i3−i3i3−i31-11-11-1000000000000
χ3422222222222-200-220000-2-222-1-1-1-1-1-1-1-1-1-1-1-1000-22-2-20000-22-22i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311111100−i3i3−i3i3−i3i31-11-11-1000000000000
χ352222222−1−i3−1+i3−1−i3−1+i322222222222−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i3222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000
χ362222222−1−i3−1+i3−1−i3−1+i3222-2-2222222−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32-2-2-2-2-2−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ372222222−1−i3−1+i3−1−i3−1+i32-2-222-2-2-2-222−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32-2-2-222−1−i3−1+i31+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000
χ382222222−1−i3−1+i3−1−i3−1+i32-2-2-2-2-2-2-2-222−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32222-2-2−1−i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ392222222−1−i3−1+i3−1−i3−1+i3-2002-20000-2-2−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i30002-21+i31−i30000−1−i31+i3−1+i31−i3000000000000-2-21+i31+i31−i31−i3000000002-2−1−i31+i3−1+i31−i3000000000000
χ402222222−1−i3−1+i3−1−i3−1+i3-2002-20000-2-2−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i320002-21+i31−i30000−1−i31+i3−1+i31−i3−i3−i3i3i3−3+i32−3+i323−i323−i323+i323+i32−3−i32−3−i3211−1−i32−1−i32−1+i32−1+i3200−i3i3−3+i323−i323+i32−3−i32-111+i32−1−i321−i32−1+i32000000000000
χ412222222−1−i3−1+i3−1−i3−1+i3-2002-20000-2-2−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i320002-21+i31−i30000−1−i31+i3−1+i31−i3i3i3−i3−i33−i323−i32−3+i32−3+i32−3−i32−3−i323+i323+i3211−1−i32−1−i32−1+i32−1+i3200i3−i33−i32−3+i32−3−i323+i32-111+i32−1−i321−i32−1+i32000000000000
χ422222222−1−i3−1+i3−1−i3−1+i3-200-220000-2-2−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i3000-221+i31−i300001+i3−1−i31−i3−1+i3000000000000-2-21+i31+i31−i31−i300000000-221+i3−1−i31−i3−1+i3000000000000
χ432222222−1−i3−1+i3−1−i3−1+i3-200-220000-2-2−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32000-221+i31−i300001+i3−1−i31−i3−1+i3−i3−i3i3i3−3+i32−3+i323−i323−i323+i323+i32−3−i32−3−i3211−1−i32−1−i32−1+i32−1+i3200i3−i33−i32−3+i32−3−i323+i321-1−1−i321+i32−1+i321−i32000000000000
χ442222222−1−i3−1+i3−1−i3−1+i3-200-220000-2-2−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32000-221+i31−i300001+i3−1−i31−i3−1+i3i3i3−i3−i33−i323−i32−3+i32−3+i32−3−i32−3−i323+i323+i3211−1−i32−1−i32−1+i32−1+i3200−i3i3−3+i323−i323+i32−3−i321-1−1−i321+i32−1+i321−i32000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.