Finite Group Databasebeta

← Group #11721351

Character table — Group #11721351

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111333333333334446666666666666666661212121212121212121212484848484848484848484848
order1332336666666626644121212121212121212121212121212124661212121212121212333333666666
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ31111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ411111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ511111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32
χ611111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32
χ71111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−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+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ81111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−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+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32
χ91111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−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+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321
χ101111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32
χ111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i32−1−i32−1+i321−1+i321−1−i321+i321−i32-11−i32-11+i32
χ121111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i32−1+i321−1−i32−1−i32−1+i3211−i32-11+i321+i321−i32-1
χ131111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+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−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ141111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+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−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321
χ151111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+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−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32
χ161111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32
χ171111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i32−1−i321−1+i32−1+i32−1−i3211+i32-11−i321−i321+i32-1
χ181111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i32−1+i32−1−i321−1−i321−1+i321−i321+i32-11+i32-11−i32
χ1933333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1000000000000
χ2033333333333333-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-3-311111111000000000000
χ213333−3−3i32−3+3i3233−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32333-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-1−3−3i32−3+3i32-1-11+i321+i321+i321−i321−i321−i32000000000000
χ223333−3−3i32−3+3i3233−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-3-3-3-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i3213+3i323−3i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000
χ233333−3+3i32−3−3i3233−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32333-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-1−3+3i32−3−3i32-1-11−i321−i321−i321+i321+i321+i32000000000000
χ243333−3+3i32−3−3i3233−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-3-3-3-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i3213−3i323+3i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000
χ253−3−3i32−3+3i32300−3−3i32−3+3i320000003−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i32000000000000300−3−3i32−3+3i32000000000000000000
χ263−3−3i32−3+3i32300−3−3i32−3+3i320000003−3−3i32−3+3i32-1-11+i321+i321−i321−i3222−1−i3−1−i3−1+i3−1+i322−1−i3−1−i3−1+i3−1+i3-1001+i321−i322−1−i3−1+i32−1−i3−1+i3000000000000
χ273−3−3i32−3+3i32300−3−3i32−3+3i320000003−3−3i32−3+3i32-1-11+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i322−1+i3−1+i322−1−i3−1−i3-1001+i321−i32−1−i3−1+i32−1+i32−1−i3000000000000
χ283−3−3i32−3+3i32300−3−3i32−3+3i320000003−3−3i32−3+3i32-1-11+i321+i321−i321−i32−1+i3−1+i322−1−i3−1−i3−1−i3−1−i3−1+i3−1+i322-1001+i321−i32−1+i32−1−i3−1−i3−1+i32000000000000
χ293−3−3i32−3+3i32300−3−3i32−3+3i32000000-33+3i323−3i3233−3−3i32−3−3i32−3+3i32−3+3i32000000000000-3003+3i323−3i32000000000000000000
χ303−3−3i32−3+3i32300−3−3i32−3+3i32000000-33+3i323−3i32-1-11+i321+i321−i321−i3222−1−i3−1−i3−1+i3−1+i322−1−i3−1−i3−1+i3−1+i3100−1−i32−1+i32-21+i31−i3-21+i31−i3000000000000
χ313−3−3i32−3+3i32300−3−3i32−3+3i32000000-33+3i323−3i32-1-11+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i322−1+i3−1+i322−1−i3−1−i3100−1−i32−1+i321+i31−i3-21−i3-21+i3000000000000
χ323−3−3i32−3+3i32300−3−3i32−3+3i32000000-33+3i323−3i32-1-11+i321+i321−i321−i32−1+i3−1+i322−1−i3−1−i3−1−i3−1−i3−1+i3−1+i322100−1−i32−1+i321−i3-21+i31+i31−i3-2000000000000
χ333−3+3i32−3−3i32300−3+3i32−3−3i320000003−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i32000000000000300−3+3i32−3−3i32000000000000000000
χ343−3+3i32−3−3i32300−3+3i32−3−3i320000003−3+3i32−3−3i32-1-11−i321−i321+i321+i3222−1+i3−1+i3−1−i3−1−i322−1+i3−1+i3−1−i3−1−i3-1001−i321+i322−1+i3−1−i32−1+i3−1−i3000000000000
χ353−3+3i32−3−3i32300−3+3i32−3−3i320000003−3+3i32−3−3i32-1-11−i321−i321+i321+i32−1−i3−1−i322−1+i3−1+i3−1+i3−1+i3−1−i3−1−i322-1001−i321+i32−1−i32−1+i3−1+i3−1−i32000000000000
χ363−3+3i32−3−3i32300−3+3i32−3−3i320000003−3+3i32−3−3i32-1-11−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i322−1−i3−1−i322−1+i3−1+i3-1001−i321+i32−1+i3−1−i32−1−i32−1+i3000000000000
χ373−3+3i32−3−3i32300−3+3i32−3−3i32000000-33−3i323+3i3233−3+3i32−3+3i32−3−3i32−3−3i32000000000000-3003−3i323+3i32000000000000000000
χ383−3+3i32−3−3i32300−3+3i32−3−3i32000000-33−3i323+3i32-1-11−i321−i321+i321+i3222−1+i3−1+i3−1−i3−1−i322−1+i3−1+i3−1−i3−1−i3100−1+i32−1−i32-21−i31+i3-21−i31+i3000000000000
χ393−3+3i32−3−3i32300−3+3i32−3−3i32000000-33−3i323+3i32-1-11−i321−i321+i321+i32−1−i3−1−i322−1+i3−1+i3−1+i3−1+i3−1−i3−1−i322100−1+i32−1−i321+i3-21−i31−i31+i3-2000000000000
χ403−3+3i32−3−3i32300−3+3i32−3−3i32000000-33−3i323+3i32-1-11−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i322−1−i3−1−i322−1+i3−1+i3100−1+i32−1−i321−i31+i3-21+i3-21−i3000000000000
χ41666-266-2-2-2-2-2-2-2-20002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000
χ42666-266-2-2-2-2-2-2-2-2000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000
χ43666-2−3−3i3−3+3i3-2-21+i31+i31+i31−i31−i31−i30002i−2i2i−2i2i−2i2ζ11−2ζ112ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ72ζ7−2ζ700000000000000000000000
χ44666-2−3−3i3−3+3i3-2-21+i31+i31+i31−i31−i31−i3000−2i2i−2i2i−2i2i−2ζ112ζ11−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7−2ζ72ζ700000000000000000000000
χ45666-2−3+3i3−3−3i3-2-21−i31−i31−i31+i31+i31+i30002i−2i2i−2i2i−2i2ζ7−2ζ72ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ112ζ11−2ζ1100000000000000000000000
χ46666-2−3+3i3−3−3i3-2-21−i31−i31−i31+i31+i31+i3000−2i2i−2i2i−2i2i−2ζ72ζ7−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11−2ζ112ζ1100000000000000000000000
χ476−3−3i3−3+3i3-2001+i31−i34−2−2i3−2+2i34−2−2i3−2+2i30002i−2i2ζ11−2ζ112ζ7−2ζ72ζ7−2ζ72i−2i2ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72i−2i00000000000000000000000
χ486−3−3i3−3+3i3-2001+i31−i34−2−2i3−2+2i34−2−2i3−2+2i3000−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7−2i2i−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2i2i00000000000000000000000
χ496−3−3i3−3+3i3-2001+i31−i3−2−2i3−2+2i34−2+2i34−2−2i30002i−2i2ζ11−2ζ112ζ7−2ζ72i−2i2ζ11−2ζ112ζ7−2ζ72i−2i2ζ11−2ζ112ζ7−2ζ700000000000000000000000
χ506−3−3i3−3+3i3-2001+i31−i3−2−2i3−2+2i34−2+2i34−2−2i3000−2i2i−2ζ112ζ11−2ζ72ζ7−2i2i−2ζ112ζ11−2ζ72ζ7−2i2i−2ζ112ζ11−2ζ72ζ700000000000000000000000
χ516−3−3i3−3+3i3-2001+i31−i3−2+2i34−2−2i3−2−2i3−2+2i340002i−2i2ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72i−2i2ζ7−2ζ72i−2i2ζ11−2ζ1100000000000000000000000
χ526−3−3i3−3+3i3-2001+i31−i3−2+2i34−2−2i3−2−2i3−2+2i34000−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2i2i−2ζ72ζ7−2i2i−2ζ112ζ1100000000000000000000000
χ536−3+3i3−3−3i3-2001−i31+i34−2+2i3−2−2i34−2+2i3−2−2i30002i−2i2ζ7−2ζ72ζ11−2ζ112ζ11−2ζ112i−2i2ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112i−2i00000000000000000000000
χ546−3+3i3−3−3i3-2001−i31+i34−2+2i3−2−2i34−2+2i3−2−2i3000−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11−2i2i−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2i2i00000000000000000000000
χ556−3+3i3−3−3i3-2001−i31+i3−2−2i34−2+2i3−2+2i3−2−2i340002i−2i2ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112i−2i2ζ11−2ζ112i−2i2ζ7−2ζ700000000000000000000000
χ566−3+3i3−3−3i3-2001−i31+i3−2−2i34−2+2i3−2+2i3−2−2i34000−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2i2i−2ζ112ζ11−2i2i−2ζ72ζ700000000000000000000000
χ576−3+3i3−3−3i3-2001−i31+i3−2+2i3−2−2i34−2−2i34−2+2i30002i−2i2ζ7−2ζ72ζ11−2ζ112i−2i2ζ7−2ζ72ζ11−2ζ112i−2i2ζ7−2ζ72ζ11−2ζ1100000000000000000000000
χ586−3+3i3−3−3i3-2001−i31+i3−2+2i3−2−2i34−2−2i34−2+2i3000−2i2i−2ζ72ζ7−2ζ112ζ11−2i2i−2ζ72ζ7−2ζ112ζ11−2i2i−2ζ72ζ7−2ζ112ζ1100000000000000000000000

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