Finite Group Databasebeta

← Group #72222836

Character table — Group #72222836

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112233336688881212121216161616161616161616161624242424242424242424242424243232323232323232323232326464646464646464
order1222442222442244444433444466666622224444444444666612121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111111111−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111111111111111−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ611111111111111111111−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ7111111111111-1-1-1-1-1-1-1-11111-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ8111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ9111111111111-1-1-1-1-1-1-1-1−1−i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-111-1-1-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ10111111111111-1-1-1-1-1-1-1-1−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-11111111+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ11111111111111-1-1-1-1-1-1-1-1−1+i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-111-1-1-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ12111111111111-1-1-1-1-1-1-1-1−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-11111111−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ131111-1-11111-1-111-1-1-1-1-1-1111-11-111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11-11-11-11-1
χ141111-1-11111-1-111-1-1-1-1-1-111-11-11111111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-11-11
χ151111-1-11111-1-111-1-1-1-1-1-1−1−i32−1+i321-11-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-11111-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ161111-1-11111-1-111-1-1-1-1-1-1−1−i32−1+i32-11-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111111-1-1-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ171111-1-11111-1-111-1-1-1-1-1-1−1+i32−1−i321-11-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-11111-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ181111-1-11111-1-111-1-1-1-1-1-1−1+i32−1−i32-11-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111111-1-1-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ191111-1-11111-1-1-1-1111111111-1-1111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111-11-1-11-11
χ201111-1-11111-1-1-1-111111111-111-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-11-111-11-1
χ211111-1-11111-1-1-1-1111111−1−i32−1+i321-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-111-1-1-1-1-1-1111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ221111-1-11111-1-1-1-1111111−1−i32−1+i32-111-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1-1-111-1-11+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ231111-1-11111-1-1-1-1111111−1+i32−1−i321-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-111-1-1-1-1-1-1111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ241111-1-11111-1-1-1-1111111−1+i32−1−i32-111-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-1-1-111-1-11−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ252-22-2002-22-200002i−2i2i2i−2i−2i220000-2-222-2-200002-2000000000000002i−2i002i−2i00000000
χ262-22-2002-22-200002i−2i2i2i−2i−2i−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i300002-2000000000000002ζ11−2ζ11002ζ7−2ζ700000000
χ272-22-2002-22-200002i−2i2i2i−2i−2i−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i300002-2000000000000002ζ7−2ζ7002ζ11−2ζ1100000000
χ282-22-2002-22-20000−2i2i−2i−2i2i2i220000-2-222-2-200002-200000000000000−2i2i00−2i2i00000000
χ292-22-2002-22-20000−2i2i−2i−2i2i2i−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i300002-200000000000000−2ζ112ζ1100−2ζ72ζ700000000
χ302-22-2002-22-20000−2i2i−2i−2i2i2i−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i300002-200000000000000−2ζ72ζ700−2ζ112ζ1100000000
χ313333333333333333-1-1-1-1003333000000-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ323333333333333333-1-1-1-100-3-3-3-30000001111-1-1-1-1-1-1111100000000000000000000
χ33333333333333-3-3-3-311110033-3-3000000-1-1-1-1-1-111-1-1111100000000000000000000
χ34333333333333-3-3-3-3111100-3-3330000001111-1-111-1-1-1-1-1-100000000000000000000
χ353333-3-33333-3-333-3-31111003-33-3000000-1-111-1-1-1-111-1-11100000000000000000000
χ363333-3-33333-3-333-3-3111100-33-3300000011-1-1-1-1-1-11111-1-100000000000000000000
χ373333-3-33333-3-3-3-333-1-1-1-1003-3-33000000-1-111-1-1111111-1-100000000000000000000
χ383333-3-33333-3-3-3-333-1-1-1-100-333-300000011-1-1-1-11111-1-11100000000000000000000
χ3944-4-4004-4-44004-4000000-2-20000-2-22222000000000000002-22-20000000000000000
χ4044-4-4004-4-44004-40000001+i31−i300001+i31−i3−1−i3−1+i3−1−i3−1+i300000000000000−1−i31+i3−1+i31−i30000000000000000
χ4144-4-4004-4-44004-40000001−i31+i300001−i31+i3−1+i3−1−i3−1+i3−1−i300000000000000−1+i31−i3−1−i31+i30000000000000000
χ4244-4-4004-4-4400-44000000-2-20000-2-2222200000000000000-22-220000000000000000
χ4344-4-4004-4-4400-440000001+i31−i300001+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000001+i3−1−i31−i3−1+i30000000000000000
χ4444-4-4004-4-4400-440000001−i31+i300001−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000001−i3−1+i31+i3−1−i30000000000000000
χ454-4-444-444-4-44-400000000-2-200002222-2-20000000000000000002-2002-20000000000
χ464-4-444-444-4-44-4000000001+i31−i30000−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000000000−1−i31+i300−1+i31−i30000000000
χ474-4-444-444-4-44-4000000001−i31+i30000−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000000000−1+i31−i300−1−i31+i30000000000
χ484-4-44-4444-4-4-4400000000-2-200002222-2-2000000000000000000-2200-220000000000
χ494-4-44-4444-4-4-44000000001+i31−i30000−1−i3−1+i3−1−i3−1+i31+i31−i30000000000000000001+i3−1−i3001−i3−1+i30000000000
χ504-4-44-4444-4-4-44000000001−i31+i30000−1+i3−1−i3−1+i3−1−i31−i31+i30000000000000000001−i3−1+i3001+i3−1−i30000000000
χ516-66-6006-66-600006i−6i−2i−2i2i2i0000000000000000-220000000000000000000000000000
χ526-66-6006-66-60000−6i6i2i2i−2i−2i0000000000000000-220000000000000000000000000000
χ536-6-666-6-2-222-2200002-22-20000000000002-22-2002-2002-22-200000000000000000000
χ546-6-666-6-2-222-2200002-22-2000000000000-22-22002-200-22-2200000000000000000000
χ556-6-666-6-2-222-220000-22-220000000000002-22-200-2200-22-2200000000000000000000
χ566-6-666-6-2-222-220000-22-22000000000000-22-2200-22002-22-200000000000000000000
χ576-6-66-66-2-2222-200002-22-20000000000002-2-2200-2200-222-200000000000000000000
χ586-6-66-66-2-2222-200002-22-2000000000000-222-200-22002-2-2200000000000000000000
χ596-6-66-66-2-2222-20000-22-220000000000002-2-22002-2002-2-2200000000000000000000
χ606-6-66-66-2-2222-20000-22-22000000000000-222-2002-200-222-200000000000000000000
χ61121212121212-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000
χ6212121212-12-12-4-4-4-444000000000000000000000000000000000000000000000000000000
χ631212-12-1200-444-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ641212-12-1200-444-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6512-1212-1200-44-440000000000000000000000000000004-4000000000000000000000000
χ6612-1212-1200-44-44000000000000000000000000000000-44000000000000000000000000

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