Finite Group Databasebeta

← Group #13135631

Character table — Group #13135631

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11222223333444444444446666666666666688888121212121212121212121212121212121212121212121212121212122424242424242424242424242424727272727272727272727272
order1223666336622444121212121212669991818181818181818182666666661212121212123636363636363636363636363636363636366618181818181818181818181844441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-111-1-1-1-111111111111111-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111-1-111-1-1-1-111111111111111-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i
χ611111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii
χ711111111111-1-11-1-111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111i−i−iiii−i−i−i−iii
χ811111111111-1-11-1-111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111−iii−i−i−iiiii−i−i
χ91111111−1−i32−1+i32−1−i32−1+i3211111111111−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−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+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+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+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−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+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+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+i32111-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ121111111−1−i32−1+i32−1−i32−1+i32111-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ131111111−1−i32−1+i32−1−i32−1+i32-1-1111111111−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321−i321−i32−1−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+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32i−ii−iζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7
χ141111111−1−i32−1+i32−1−i32−1+i32-1-1111111111−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321−i321−i32−1−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+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32−ii−ii−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7
χ151111111−1−i32−1+i32−1−i32−1+i32-1-11-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-1111+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32i−i−iiζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ161111111−1−i32−1+i32−1−i32−1+i32-1-11-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-1111+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−iii−i−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ171111111−1+i32−1−i32−1+i32−1−i3211111111111−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+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−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−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−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+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−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−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−i32111-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ201111111−1+i32−1−i32−1+i32−1−i32111-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ211111111−1+i32−1−i32−1+i32−1−i32-1-1111111111−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321+i321+i32−1+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−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32i−ii−iζ7ζ11−ζ7−ζ11ζ7ζ11−ζ7−ζ11
χ221111111−1+i32−1−i32−1+i32−1−i32-1-1111111111−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321+i321+i32−1+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−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32−ii−ii−ζ7−ζ11ζ7ζ11−ζ7−ζ11ζ7ζ11
χ231111111−1+i32−1−i32−1+i32−1−i32-1-11-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-1111−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32i−i−iiζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11
χ241111111−1+i32−1−i32−1+i32−1−i32-1-11-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-1111−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−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
χ2622222222222222-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-222-2-2222222-2-2-2-2-1-1-1-1-1-1111111111111-2-2-1-1-1-1-1-1111111000000000000
χ27222222222222-2-200-2-200002222222222222202-2002-22-2-2-20000-2-2-2-2-2-2000000000000002-22-22-2000000000000000000
χ28222222222222-2-200-2-2000022-1-1-1-1-1-1-1-1-1-1-1-102-2002-22-2-2-20000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300-11-11-11−i3i3−i3i3−i3i3000000000000
χ29222222222222-2-200-2-2000022-1-1-1-1-1-1-1-1-1-1-1-102-2002-22-2-2-20000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300-11-11-11i3−i3i3−i3i3−i3000000000000
χ3022222222222-22-200-2-20000222222222222220-2200-22-22-2-20000-2-2-2-2-2-200000000000000-22-22-22000000000000000000
χ3122222222222-22-200-2-2000022-1-1-1-1-1-1-1-1-1-1-1-10-2200-22-22-2-20000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3001-11-11-1i3−i3i3−i3i3−i3000000000000
χ3222222222222-22-200-2-2000022-1-1-1-1-1-1-1-1-1-1-1-10-2200-22-22-2-20000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3001-11-11-1−i3i3−i3i3−i3i3000000000000
χ3322222222222-2-222222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111111111000000000000
χ3422222222222-2-22-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-12-2-222-2-2-2-222-2-2-2-2-1-1-1-1-1-111111111111122111111-1-1-1-1-1-1000000000000
χ352222222−1−i3−1+i3−1−i3−1+i322222222222−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i3222222−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−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+i3222-2-222-2-2-2-2−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32-222-2-2−1−i3−1−i3−1+i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ372222222−1−i3−1+i3−1−i3−1+i32-2-200-2-20000−1−i3−1+i32−1−i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i302-200−1−i31+i3−1+i31−i31+i31−i30000-2-21+i31+i31−i31−i3000000000000002-2−1−i31+i3−1+i31−i3000000000000000000
χ382222222−1−i3−1+i3−1−i3−1+i32-2-200-2-20000−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i3202-200−1−i31+i3−1+i31−i31+i31−i3000011−1−i32−1−i32−1+i32−1+i32−i3−i3i3i3−3+i32−3+i323−i323−i323+i323+i32−3−i32−3−i3200-111+i32−1−i321−i32−1+i32−i3i3−3+i323−i323+i32−3−i32000000000000
χ392222222−1−i3−1+i3−1−i3−1+i32-2-200-2-20000−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i3202-200−1−i31+i3−1+i31−i31+i31−i3000011−1−i32−1−i32−1+i32−1+i32i3i3−i3−i33−i323−i32−3+i32−3+i32−3−i32−3−i323+i323+i3200-111+i32−1−i321−i32−1+i32i3−i33−i32−3+i32−3−i323+i32000000000000
χ402222222−1−i3−1+i3−1−i3−1+i3-22-200-2-20000−1−i3−1+i32−1−i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30-22001+i3−1−i31−i3−1+i31+i31−i30000-2-21+i31+i31−i31−i300000000000000-221+i3−1−i31−i3−1+i3000000000000000000
χ412222222−1−i3−1+i3−1−i3−1+i3-22-200-2-20000−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320-22001+i3−1−i31−i3−1+i31+i31−i3000011−1−i32−1−i32−1+i32−1+i32−i3−i3i3i3−3+i32−3+i323−i323−i323+i323+i32−3−i32−3−i32001-1−1−i321+i32−1+i321−i32i3−i33−i32−3+i32−3−i323+i32000000000000
χ422222222−1−i3−1+i3−1−i3−1+i3-22-200-2-20000−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i320-22001+i3−1−i31−i3−1+i31+i31−i3000011−1−i32−1−i32−1+i32−1+i32i3i3−i3−i33−i323−i32−3+i32−3+i32−3−i32−3−i323+i323+i32001-1−1−i321+i32−1+i321−i32−i3i3−3+i323−i323+i32−3−i32000000000000
χ432222222−1−i3−1+i3−1−i3−1+i3-2-2222222222−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32-2-2-2-2-21+i31+i31−i31−i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ442222222−1−i3−1+i3−1−i3−1+i3-2-22-2-222-2-2-2-2−1−i3−1+i3-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i322-2-2221+i31+i31−i31−i3−1−i3−1+i31+i31+i31−i31−i3-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000
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χ462222222−1+i3−1−i3−1+i3−1−i3222-2-222-2-2-2-2−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32-222-2-2−1+i3−1+i3−1−i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000
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χ532222222−1+i3−1−i3−1+i3−1−i3-2-2222222222−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32-2-2-2-2-21−i31−i31+i31+i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ542222222−1+i3−1−i3−1+i3−1−i3-2-22-2-222-2-2-2-2−1+i3−1−i3-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i322-2-2221−i31−i31+i31+i3−1+i3−1−i31−i31−i31+i31+i3-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.