Finite Group Databasebeta

← Group #72342955

Character table — Group #72342955

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11266881212121232323232323232324848484848484848481126688121212123232323232323232484848484848484848
order12424882244361212242424242444448882242488224466121224242424244444888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-1-1-1-1-11-1-11111111111111111111-1-1-1-1-1-11-1-1
χ311111-1-111111111-1-1-1-11-11-1-1-1-11111111-1-111111111-1-1-1-11-11-1-1-1-111
χ411111-1-111111111-1-1-1-1-11-1111-1-1-111111-1-111111111-1-1-1-1-11-1111-1-1-1
χ522222222222-1-1-1-1-1-1-1-100000020022222222222-1-1-1-1-1-1-1-1000000200
χ622222-2-22222-1-1-1-11111000000-20022222-2-22222-1-1-1-11111000000-200
χ722-22-200-22-2222-2-2000000000000022-22-200-22-2222-2-20000000000000
χ822-22-200-22-22-1-11133−3−300000000022-22-200-22-22-1-11133−3−3000000000
χ922-22-200-22-22-1-111−3−33300000000022-22-200-22-22-1-111−3−333000000000
χ103333333-1-1-1-1000000001111-1-1-1-1-13333333-1-1-1-1000000001111-1-1-1-1-1
χ113333333-1-1-1-100000000-1-1-1-111-1113333333-1-1-1-100000000-1-1-1-111-111
χ1233333-3-3-1-1-1-1000000001-11-1111-1-133333-3-3-1-1-1-1000000001-11-1111-1-1
χ1333333-3-3-1-1-1-100000000-11-11-1-111133333-3-3-1-1-1-100000000-11-11-1-1111
χ14666-2-2002-2-220000000020-2000000666-2-2002-2-220000000020-2000000
χ15666-2-2002-2-2200000000-202000000666-2-2002-2-2200000000-202000000
χ16666-2-200-222-200000000020-200000666-2-200-222-200000000020-200000
χ17666-2-200-222-2000000000-20200000666-2-200-222-2000000000-20200000
χ1866-66-6002-22-20000000000000000066-66-6002-22-200000000000000000
χ1966-6-220022-2-20000000000002-200066-6-220022-2-20000000000002-2000
χ2066-6-220022-2-2000000000000-2200066-6-220022-2-2000000000000-22000
χ2166-6-2200-2-2220000000000000002-266-6-2200-2-2220000000000000002-2
χ2266-6-2200-2-222000000000000000-2266-6-2200-2-222000000000000000-22
χ238-8000−2i22i200002-200−i2i2−i2i20000000008-8000−2i22i200002-200−i2i2−i2i2000000000
χ248-8000−2i22i20000-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000008-8000−2i22i20000-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000
χ258-8000−2i22i20000-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000008-8000−2i22i20000-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000
χ268-80002i2−2i200002-200i2−i2i2−i20000000008-80002i2−2i200002-200i2−i2i2−i2000000000
χ278-80002i2−2i20000-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000008-80002i2−2i20000-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000
χ288-80002i2−2i20000-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000008-80002i2−2i20000-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000
χ291111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ301111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111
χ3111111-1-111111111-1-1-1-11-11-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-11-11111-1-1
χ3211111-1-111111111-1-1-1-1-11-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11-1-1-1111
χ3322222222222-1-1-1-1-1-1-1-1000000200-2-2-2-2-2-2-2-2-2-2-211111111000000-200
χ3422222-2-22222-1-1-1-11111000000-200-2-2-2-2-222-2-2-2-21111-1-1-1-1000000200
χ3522-22-200-22-2222-2-20000000000000-2-22-22002-22-2-2-2220000000000000
χ3622-22-200-22-22-1-11133−3−3000000000-2-22-22002-22-211-1-1−3−333000000000
χ3722-22-200-22-22-1-111−3−333000000000-2-22-22002-22-211-1-133−3−3000000000
χ383333333-1-1-1-1000000001111-1-1-1-1-1-3-3-3-3-3-3-3111100000000-1-1-1-111111
χ393333333-1-1-1-100000000-1-1-1-111-111-3-3-3-3-3-3-31111000000001111-1-11-1-1
χ4033333-3-3-1-1-1-1000000001-11-1111-1-1-3-3-3-3-333111100000000-11-11-1-1-111
χ4133333-3-3-1-1-1-100000000-11-11-1-1111-3-3-3-3-3331111000000001-11-111-1-1-1
χ42666-2-2002-2-220000000020-2000000-6-6-62200-222-200000000-202000000
χ43666-2-2002-2-2200000000-202000000-6-6-62200-222-20000000020-2000000
χ44666-2-200-222-200000000020-200000-6-6-622002-2-22000000000-20200000
χ45666-2-200-222-2000000000-20200000-6-6-622002-2-2200000000020-200000
χ4666-66-6002-22-200000000000000000-6-66-6600-22-2200000000000000000
χ4766-6-220022-2-20000000000002-2000-6-662-200-2-222000000000000-22000
χ4866-6-220022-2-2000000000000-22000-6-662-200-2-2220000000000002-2000
χ4966-6-2200-2-2220000000000000002-2-6-662-20022-2-2000000000000000-22
χ5066-6-2200-2-222000000000000000-22-6-662-20022-2-20000000000000002-2
χ518-8000−2i22i200002-200−i2i2−i2i2000000000-880002i2−2i20000-2200i2−i2i2−i2000000000
χ528-8000−2i22i20000-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000-880002i2−2i200001-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000
χ538-8000−2i22i20000-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000-880002i2−2i200001-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000
χ548-80002i2−2i200002-200i2−i2i2−i2000000000-88000−2i22i20000-2200−i2i2−i2i2000000000
χ558-80002i2−2i20000-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000-88000−2i22i200001-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000
χ568-80002i2−2i20000-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000-88000−2i22i200001-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000

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