Finite Group Databasebeta

← Group #13141705

Character table — Group #13141705

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122222333344444666666666666888888881212121212121212121212121224242424242424242424242424242424242424242424363636363636363636363636363636363636727272
order122344633664461212669991212121218181888121224242424121212121818183636363636362424242436363636363672727272727272727272727222444466661212121212121212266
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-11111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-11111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111
χ511111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-11-11111-1-111-1-11111-1-1-1
χ611111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-1111
χ711111111111-1-1111111111111111-11-1-1-1-111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-11-1-1-111-1-111-1-1-1-1-1-1111
χ811111111111-1-1111111111111111-11-1-1-1-111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1111-1-111-1-1111111-1-1-1
χ91111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−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+i3211−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ101111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−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+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32-11+i321−i32
χ111111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11+i321−i32
χ121111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-1-1-1111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ131111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321-11-111−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ141111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-11-11-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32
χ151111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321-11-1-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i321−1−i32−1+i32
χ161111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-11-11111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ171111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+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−i3211−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ181111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+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−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32-11−i321+i32
χ191111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11−i321+i32
χ201111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1-1-1111−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ211111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321-11-111−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ221111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-11-11-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32
χ231111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321-11-1-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i321−1+i32−1−i32
χ241111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-11-11111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ25222222222222222222-1-1-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ26222222222222222222-1-1-12222-1-1-1-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000000
χ2722222222222-2-222222-1-1-12222-1-1-12-2-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-122-2-2111111-1-1-1-1-1-1111111000000000000000000000
χ2822222222222-2-222222-1-1-12222-1-1-1-22-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-222111111111111-1-1-1-1-1-1000000000000000000000
χ292222222−1−i3−1+i3−1−i3−1+i322222−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i3222222222−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000000
χ302222222−1−i3−1+i3−1−i3−1+i322222−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-2-222-2-2-2-2−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i321+i31−i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ312222222−1−i3−1+i3−1−i3−1+i3-2-2222−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i322-2-2-222-2-21+i31+i31−i31−i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ322222222−1−i3−1+i3−1−i3−1+i3-2-2222−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-22-2-2-2-2221+i31+i31−i31−i3-11+i321−i32-1-11+i321+i321−i321−i321+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000000
χ332222222−1+i3−1−i3−1+i3−1−i322222−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i3222222222−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000000
χ342222222−1+i3−1−i3−1+i3−1−i322222−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32-2-222-2-2-2-2−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i321−i31+i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ352222222−1+i3−1−i3−1+i3−1−i3-2-2222−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i322-2-2-222-2-21−i31−i31+i31+i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ362222222−1+i3−1−i3−1+i3−1−i3-2-2222−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32-22-2-2-2-2221−i31−i31+i31+i3-11−i321+i32-1-11−i321−i321+i321+i321−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000000
χ372222-2-2222222-22-2-222222-2-2-2-2222002-200002-22-2222-2-2-2-2-2-200002-22-22-2000000000000000000000000000000000
χ382222-2-2222222-22-2-222-1-1-1-2-2-2-2-1-1-1002-200002-22-2-1-1-11111110000-11-11-113−33−33−33−33−33−3000000000000000000000
χ392222-2-2222222-22-2-222-1-1-1-2-2-2-2-1-1-1002-200002-22-2-1-1-11111110000-11-11-11−33−33−33−33−33−33000000000000000000000
χ402222-2-222222-222-2-222222-2-2-2-222200-220000-22-22222-2-2-2-2-2-20000-22-22-22000000000000000000000000000000000
χ412222-2-222222-222-2-222-1-1-1-2-2-2-2-1-1-100-220000-22-22-1-1-111111100001-11-11-13−33−33−3−33−33−33000000000000000000000
χ422222-2-222222-222-2-222-1-1-1-2-2-2-2-1-1-100-220000-22-22-1-1-111111100001-11-11-1−33−33−333−33−33−3000000000000000000000
χ432222-2-22−1−i3−1+i3−1−i3−1+i32-22-2-2−1−i3−1+i32−1−i3−1+i31+i31+i31−i31−i32−1−i3−1+i3002-20000−1−i31+i3−1+i31−i32−1−i3−1+i3-2-21+i31+i31−i31−i300002-2−1−i31+i3−1+i31−i3000000000000000000000000000000000
χ442222-2-22−1−i3−1+i3−1−i3−1+i32-22-2-2−1−i3−1+i3-11+i321−i321+i31+i31−i31−i3-11+i321−i32002-20000−1−i31+i3−1+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i320000-111+i32−1−i321−i32−1+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000000
χ452222-2-22−1−i3−1+i3−1−i3−1+i32-22-2-2−1−i3−1+i3-11+i321−i321+i31+i31−i31−i3-11+i321−i32002-20000−1−i31+i3−1+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i320000-111+i32−1−i321−i32−1+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000000
χ462222-2-22−1−i3−1+i3−1−i3−1+i3-222-2-2−1−i3−1+i32−1−i3−1+i31+i31+i31−i31−i32−1−i3−1+i300-2200001+i3−1−i31−i3−1+i32−1−i3−1+i3-2-21+i31+i31−i31−i30000-221+i3−1−i31−i3−1+i3000000000000000000000000000000000
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χ512222-2-22−1+i3−1−i3−1+i3−1−i32-22-2-2−1+i3−1−i3-11−i321+i321−i31−i31+i31+i3-11−i321+i32002-20000−1+i31−i3−1−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i320000-111−i32−1+i321+i32−1−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000000000
χ522222-2-22−1+i3−1−i3−1+i3−1−i3-222-2-2−1+i3−1−i32−1+i3−1−i31−i31−i31+i31+i32−1+i3−1−i300-2200001−i3−1+i31+i3−1−i32−1+i3−1−i3-2-21−i31−i31+i31+i30000-221−i3−1+i31+i3−1−i3000000000000000000000000000000000
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χ6322-22-222−1−i3−1+i3−1−i3−1+i300-2-221+i31−i32−1−i3−1+i31+i3−1−i31−i3−1+i32−1−i3−1+i3000000000000-21+i31−i3-221+i3−1−i31−i3−1+i3000000000000000000000020-2000−1−i3−1+i3001+i31−i3000000000
χ6422-22-222−1−i3−1+i3−1−i3−1+i300-2-221+i31−i32−1−i3−1+i31+i3−1−i31−i3−1+i32−1−i3−1+i3000000000000-21+i31−i3-221+i3−1−i31−i3−1+i30000000000000000000000-2020001+i31−i300−1−i3−1+i3000000000
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χ6844-444-44−2−2i3−2+2i3−2−2i3−2+2i300-44-42+2i32−2i3-21+i31−i3−2−2i32+2i3−2+2i32−2i3-21+i31−i30000000000002−1−i3−1+i3-221+i3−1−i31−i3−1+i30000000000000000000000000000000000000000000
χ6944-444-44−2+2i3−2−2i3−2+2i3−2−2i300-44-42−2i32+2i3-21−i31+i3−2+2i32−2i3−2−2i32+2i3-21−i31+i30000000000002−1+i3−1−i3-221−i3−1+i31+i3−1−i30000000000000000000000000000000000000000000
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χ7144-44-444−2−2i3−2+2i3−2−2i3−2+2i300-4-442+2i32−2i3-21+i31−i32+2i3−2−2i32−2i3−2+2i3-21+i31−i30000000000002−1−i3−1+i32-2−1−i31+i3−1+i31−i30000000000000000000000000000000000000000000
χ7244-44-444−2+2i3−2−2i3−2+2i3−2−2i300-4-442−2i32+2i3-21−i31+i32−2i3−2+2i32+2i3−2−2i3-21−i31+i30000000000002−1+i3−1−i32-2−1+i31−i3−1−i31+i30000000000000000000000000000000000000000000
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χ9224-240-1200120000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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