Finite Group Databasebeta

← Group #11721536

Character table — Group #11721536

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size1122233334444446666666688121212121212121212121212121212181818181818242424242424363636363636363636
order12346336622812242433366612126666661212122424242424242424246612126666662466812122424
χ11111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ31111111111-1-11-1-1111111111-111-1-1111-1-1-1-1-1-1-1-1111111111-1-1-11-111-1-1-1-1-1
χ41111111111-1-11-1-1111111111-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-111111
χ5111111111-11-11-1-111111111-11-1-111111-1-1-1-1-1-1-1-1111111-1-1-1111-11-1-1-111-1-1
χ6111111111-11-11-1-111111111-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111
χ7111111111-1-1111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111
χ8111111111-1-1111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1
χ911111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ1011111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321+i321−i32
χ1111111−1−i32−1+i32−1−i32−1+i321-1-11-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-11+i321−i321-1−1−i32−1+i32-11+i321−i321+i321−i32
χ1211111−1−i32−1+i32−1−i32−1+i321-1-11-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321−i321+i321−i321−1−i32−1+i32-11+i321−i32-111+i321−i321−1−i32−1+i32−1−i32−1+i32
χ1311111−1−i32−1+i32−1−i32−1+i32-11-11-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32-111+i321−i32−1−i32−1+i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32-111+i321−i32-1−1−i32−1+i321+i321−i32
χ1411111−1−i32−1+i32−1−i32−1+i32-11-11-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32-111+i321−i32−1−i32−1+i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321−i321+i321−i32-11+i321−i321−1−i32−1+i321-1−1−i32−1+i3211+i321−i32−1−i32−1+i32
χ1511111−1−i32−1+i32−1−i32−1+i32-1-111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32-11+i321−i32-11+i321−i32-1-11+i321−i3211+i321−i32−1−i32−1+i32
χ1611111−1−i32−1+i32−1−i32−1+i32-1-111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i3211−1−i32−1+i32-1−1−i32−1+i321+i321−i32
χ1711111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ1811111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−i321+i32
χ1911111−1+i32−1−i32−1+i32−1−i321-1-11-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-11−i321+i321-1−1+i32−1−i32-11−i321+i321−i321+i32
χ2011111−1+i32−1−i32−1+i32−1−i321-1-11-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321+i321−i321+i321−1+i32−1−i32-11−i321+i32-111−i321+i321−1+i32−1−i32−1+i32−1−i32
χ2111111−1+i32−1−i32−1+i32−1−i32-11-11-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32-111−i321+i32−1+i32−1−i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32-111−i321+i32-1−1+i32−1−i321−i321+i32
χ2211111−1+i32−1−i32−1+i32−1−i32-11-11-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32-111−i321+i32−1+i32−1−i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321+i321−i321+i32-11−i321+i321−1+i32−1−i321-1−1+i32−1−i3211−i321+i32−1+i32−1−i32
χ2311111−1+i32−1−i32−1+i32−1−i32-1-111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32-11−i321+i32-11−i321+i32-1-11−i321+i3211−i321+i32−1+i32−1−i32
χ2411111−1+i32−1−i32−1+i32−1−i32-1-111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i3211−1+i32−1−i32-1−1+i32−1−i321−i321+i32
χ25222222222222222-1-1-1-1-1-122222222-1-1-122-1-1-1-1-1-1000000-1-1-1-1-1-1000000000
χ262222222222-2-22-2-2-1-1-1-1-1-1222-222-2-2-1-1-1-2-2111111000000-1-1-1111000000000
χ27222222222-22-22-2-2-1-1-1-1-1-122-22-2-222-1-1-1-2-2111111000000111-1-1-1000000000
χ28222222222-2-22222-1-1-1-1-1-122-2-2-2-2-2-2-1-1-122-1-1-1-1-1-1000000111111000000000
χ2922222−1−i3−1+i3−1−i3−1+i3222222-11+i321−i32-11+i321−i32−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000-11+i321−i32-11+i321−i32000000000
χ3022222−1−i3−1+i3−1−i3−1+i32-2-22-2-2-11+i321−i32-11+i321−i32−1−i3−1+i32-2−1−i3−1+i31+i31−i3-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000-11+i321−i321−1−i32−1+i32000000000
χ3122222−1−i3−1+i3−1−i3−1+i3-22-22-2-2-11+i321−i32-11+i321−i32−1−i3−1+i3-221+i31−i3−1−i3−1+i3-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i320000001−1−i32−1+i32-11+i321−i32000000000
χ3222222−1−i3−1+i3−1−i3−1+i3-2-22222-11+i321−i32-11+i321−i32−1−i3−1+i3-2-21+i31−i31+i31−i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i320000001−1−i32−1+i321−1−i32−1+i32000000000
χ3322222−1+i3−1−i3−1+i3−1−i3222222-11−i321+i32-11−i321+i32−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000-11−i321+i32-11−i321+i32000000000
χ3422222−1+i3−1−i3−1+i3−1−i32-2-22-2-2-11−i321+i32-11−i321+i32−1+i3−1−i32-2−1+i3−1−i31−i31+i3-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000-11−i321+i321−1+i32−1−i32000000000
χ3522222−1+i3−1−i3−1+i3−1−i3-22-22-2-2-11−i321+i32-11−i321+i32−1+i3−1−i3-221−i31+i3−1+i3−1−i3-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i320000001−1+i32−1−i32-11−i321+i32000000000
χ3622222−1+i3−1−i3−1+i3−1−i3-2-22222-11−i321+i32-11−i321+i32−1+i3−1−i3-2-21−i31+i31−i31+i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i320000001−1+i32−1−i321−1+i32−1−i32000000000
χ37222-222222000-200222222-2-2000000-2-2-2000000002-222-2-2000000000000000
χ38222-222222000-200222222-2-2000000-2-2-200000000-22-2-222000000000000000
χ39222-22−1−i3−1+i3−1−i3−1+i3000-2002−1−i3−1+i32−1−i3−1+i31+i31−i3000000-21+i31−i3000000002-2−1−i3−1+i31+i31−i3000000000000000
χ40222-22−1−i3−1+i3−1−i3−1+i3000-2002−1−i3−1+i32−1−i3−1+i31+i31−i3000000-21+i31−i300000000-221+i31−i3−1−i3−1+i3000000000000000
χ41222-22−1+i3−1−i3−1+i3−1−i3000-2002−1+i3−1−i32−1+i3−1−i31−i31+i3000000-21−i31+i3000000002-2−1+i3−1−i31−i31+i3000000000000000
χ42222-22−1+i3−1−i3−1+i3−1−i3000-2002−1+i3−1−i32−1+i3−1−i31−i31+i3000000-21−i31+i300000000-221−i31+i3−1+i3−1−i3000000000000000
χ43444-444444000-400-2-2-2-2-2-2-4-400000022200000000000000000000000000000
χ44444-44−2−2i3−2+2i3−2−2i3−2+2i3000-400-21+i31−i3-21+i31−i32+2i32−2i30000002−1−i3−1+i300000000000000000000000000000
χ45444-44−2+2i3−2−2i3−2+2i3−2−2i3000-400-21−i31+i3-21−i31+i32−2i32+2i30000002−1+i3−1−i300000000000000000000000000000
χ464-440-444-4-4000000444-4-4-40000000000000000000000000000000000000000
χ474-440-444-4-4000000-2-2-22220000000000000i6−i6i6−i6i6−i6000000000000000000000
χ484-440-444-4-4000000-2-2-22220000000000000−i6i6−i6i6−i6i6000000000000000000000
χ494-440-4−2−2i3−2+2i32+2i32−2i30000004−2−2i3−2+2i3-42+2i32−2i30000000000000000000000000000000000000000
χ504-440-4−2−2i3−2+2i32+2i32−2i3000000-21+i31−i32−1−i3−1+i30000000000000i6−i6−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23000000000000000000000
χ514-440-4−2−2i3−2+2i32+2i32−2i3000000-21+i31−i32−1−i3−1+i30000000000000−i6i62ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ23000000000000000000000
χ524-440-4−2+2i3−2−2i32−2i32+2i30000004−2+2i3−2−2i3-42−2i32+2i30000000000000000000000000000000000000000
χ534-440-4−2+2i3−2−2i32−2i32+2i3000000-21−i31+i32−1+i3−1−i30000000000000i6−i6ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23000000000000000000000
χ544-440-4−2+2i3−2−2i32−2i32+2i3000000-21−i31+i32−1+i3−1−i30000000000000−i6i6−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ232ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23000000000000000000000
χ5566-36-30000666-3-3-300000000-3-3000000000000000000000000000000000000
χ5666-36-300006-6-6-33300000000-33000000000000000000000000000000000000
χ5766-36-30000-66-6-333000000003-3000000000000000000000000000000000000
χ5866-36-30000-6-66-3-3-30000000033000000000000000000000000000000000000
χ591212-6-12-600000006000000000000000000000000000000000000000000000000
χ6012-12-606000000003i6−3i60000000000000000000000000000000000000000000000
χ6112-12-60600000000−3i63i60000000000000000000000000000000000000000000000

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