Finite Group Databasebeta

← Group #97239

Character table — Group #97239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222224444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-11-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-111-1-111-1-1-11-1-11-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-111-1-1-11-1-11-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-111-1-1-1-111-1-11-1-11-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1−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
χ131111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-111-11ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-111-11−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-2-20000200-2000000000000000000
χ18222222222222-2-2-2-222-2-2-2-2220000-2002000000000000000000
χ192222222222-2-22222-2-222-2-2-2-20000-2002000000000000000000
χ202222222222-2-22222-2-2-2-2-2-2220000200-2000000000000000000
χ2122222222-2-22-222-2-22-2002-200002-200200-20000000000000000
χ2222222222-2-22-222-2-22-2002-20000-2200-20020000000000000000
χ2322222222-2-22-2-2-2222-200-22002-2000200-200000000000000000
χ2422222222-2-22-2-2-2222-200-2200-22000-200200000000000000000
χ2522222222-2-2-2222-2-2-2200-22002-2000-200200000000000000000
χ2622222222-2-2-2222-2-2-2200-2200-22000200-200000000000000000
χ2722222222-2-2-22-2-222-22002-200002-200-20020000000000000000
χ2822222222-2-2-22-2-222-22002-20000-2200200-20000000000000000
χ29444-4-44-4-4000400000-400000000000000000000000000002-22-2
χ30444-4-44-4-4000400000-40000000000000000000000000000-22-22
χ31444-4-44-4-4000-400000400000000000000000000000000002i−2i−2i2i
χ32444-4-44-4-4000-40000040000000000000000000000000000−2i2i2i−2i
χ3344-44-4-4-440000004i−4i00000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ3444-44-4-4-440000004i−4i0000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ3544-44-4-4-44000000−4i4i00000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ3644-44-4-4-44000000−4i4i0000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ374-44-44-4-4400004i−4i000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ384-44-44-4-4400004i−4i00000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ394-44-44-4-440000−4i4i000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ404-44-44-4-440000−4i4i00000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ414-4-4444-4-400400000-400000000000000000000000002-22-20000
χ424-4-4444-4-400400000-40000000000000000000000000-22-220000
χ434-4-4444-4-400-400000400000000000000000000000002i−2i−2i2i0000
χ444-4-4444-4-400-40000040000000000000000000000000−2i2i2i−2i0000
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
χ4988-8-88-88-8000000000000000000000000000000000000000000
χ508-888-8-88-8000000000000000000000000000000000000000000

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