Finite Group Databasebeta

← Group #97236

Character table — Group #97236

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222224444444422444424444444448888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-111-1-1-111-1-11-1-11-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-1-111-1-11-1-11-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-111-1-1-1-1-111-11-1-111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-111-1-1-1-1-111-11-1-11-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-111-11ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-111-11−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1111-111-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1111-111-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-2-22000000-2000000000000000000
χ18222222222222-2-2-2-222-2-2-2-222-20000002000000000000000000
χ192222222222-2-22222-2-222-2-2-2-2-20000002000000000000000000
χ202222222222-2-22222-2-2-2-2-2-2222000000-2000000000000000000
χ2122222222-2-22-222-2-22-2002-2000002-20200-20000000000000000
χ2222222222-2-22-222-2-22-2002-200000-220-20020000000000000000
χ2322222222-2-22-2-2-2222-200-220002-200200-200000000000000000
χ2422222222-2-22-2-2-2222-200-22000-2200-200200000000000000000
χ2522222222-2-2-2222-2-2-2200-220002-200-200200000000000000000
χ2622222222-2-2-2222-2-2-2200-22000-2200200-200000000000000000
χ2722222222-2-2-22-2-222-22002-2000002-20-20020000000000000000
χ2822222222-2-2-22-2-222-22002-200000-220200-20000000000000000
χ29444-4-4-44-40000004i−4i00000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ30444-4-4-44-40000004i−4i0000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ31444-4-4-44-4000000−4i4i00000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ32444-4-4-44-4000000−4i4i0000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ3344-44-4-4-44000400000-400000000000000000000000000002i−2i2i−2i
χ3444-44-4-4-44000400000-40000000000000000000000000000−2i2i−2i2i
χ3544-44-4-4-44000-400000400000000000000000000000000002-2-22
χ3644-44-4-4-44000-40000040000000000000000000000000000-222-2
χ374-44-44-4-4400400000-400000000000000000000000002i−2i2i−2i0000
χ384-44-44-4-4400400000-40000000000000000000000000−2i2i−2i2i0000
χ394-44-44-4-4400-400000400000000000000000000000002-2-220000
χ404-44-44-4-4400-40000040000000000000000000000000-222-20000
χ414-4-444-44-400004i−4i000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ424-4-444-44-400004i−4i00000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ434-4-444-44-40000−4i4i000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ444-4-444-44-40000−4i4i00000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ454-4-4-4-44444-40000000000004-400000000000000000000000000
χ464-4-4-4-44444-4000000000000-4400000000000000000000000000
χ474-4-4-4-4444-44000000004-4000000000000000000000000000000
χ484-4-4-4-4444-4400000000-44000000000000000000000000000000
χ4988-8-888-8-8000000000000000000000000000000000000000000
χ508-888-88-8-8000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.