Finite Group Databasebeta

← Group #98433

Character table — Group #98433

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-11111
χ5111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1
χ91111111111-1-111-1-1-1-1-1-11111111-1-11-1-111-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-111-1-1-1-1-1-11111111-1-11-1-111-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-111-1-1-1-1-1-111111-1-111-11-1-1-111-1ii−i−i−i−iiiii−i−i−i−iii
χ121111111111-1-111-1-1-1-1-1-111111-1-111-11-1-1-111-1−i−iiiii−i−i−i−iiiii−i−i
χ131111111111-1-111-1-1-1-1-1-11-1-1-1-111-1-11-11-1-1111ii−i−iii−i−i−i−iii−i−iii
χ141111111111-1-111-1-1-1-1-1-11-1-1-1-111-1-11-11-1-1111−i−iii−i−iiiii−i−iii−i−i
χ151111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-111-11111-1-11ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-111-11111-1-11−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2-2-222-200002222-2-20000000000000000000000
χ18222222222222-2-2-2-2-2-222-20000-2-2-2-2220000000000000000000000
χ192222222222-2-2-2-22222-2-2-2000022-2-2-220000000000000000000000
χ202222222222-2-2-2-22222-2-2-20000-2-2222-20000000000000000000000
χ2122222222-2-22-22222-2-22-2-222-2-200000020000-20000000000000000
χ2222222222-2-22-22222-2-22-2-2-2-222000000-2000020000000000000000
χ2322222222-2-22-2-2-2-2-2222-22000000000002-22-200000000000000000
χ2422222222-2-22-2-2-2-2-2222-2200000000000-22-2200000000000000000
χ2522222222-2-2-2222-2-222-22-222-2-2000000-2000020000000000000000
χ2622222222-2-2-2222-2-222-22-2-2-22200000020000-20000000000000000
χ2722222222-2-2-22-2-222-2-2-222000000000002-2-2200000000000000000
χ2822222222-2-2-22-2-222-2-2-22200000000000-222-200000000000000000
χ2922-2-2-222-22-22-2000000-22000002i−2i2i−2i000000002−22−2i2−i2i2−i200000000
χ3022-2-2-222-22-22-2000000-22000002i−2i2i−2i00000000−22−22−i2i2−i2i200000000
χ3122-2-2-222-22-22-2000000-2200000−2i2i−2i2i000000002−22−2−i2i2−i2i200000000
χ3222-2-2-222-22-22-2000000-2200000−2i2i−2i2i00000000−22−22i2−i2i2−i200000000
χ3322-2-2-222-22-2-220000002-2000002i−2i−2i2i00000000i2−i2−i2i2−222−200000000
χ3422-2-2-222-22-2-220000002-2000002i−2i−2i2i00000000−i2i2i2−i22−2−2200000000
χ3522-2-2-222-22-2-220000002-200000−2i2i2i−2i00000000i2−i2−i2i22−2−2200000000
χ3622-2-2-222-22-2-220000002-200000−2i2i2i−2i00000000−i2i2i2−i2−222−200000000
χ37444-4-4-4-4400004-40000000004i−4i0000000000000000000000000000
χ38444-4-4-4-4400004-4000000000−4i4i0000000000000000000000000000
χ39444-4-4-4-440000-4400000004i−4i000000000000000000000000000000
χ40444-4-4-4-440000-440000000−4i4i000000000000000000000000000000
χ4144-4-4-444-4-4444000000-4-4000000000000000000000000000000000
χ4244-4-4-444-4-44-4-400000044000000000000000000000000000000000
χ434-444-44-4-40000004i−4i0000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ444-444-44-4-40000004i−4i000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ454-444-44-4-4000000−4i4i0000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ464-444-44-4-4000000−4i4i000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ474-44-44-44-4000000004i−4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ484-44-44-44-4000000004i−4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ494-44-44-44-400000000−4i4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ504-44-44-44-400000000−4i4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ5188-888-8-8-8000000000000000000000000000000000000000000000
χ528-8-88-8-888000000000000000000000000000000000000000000000
χ538-8-8-888-88000000000000000000000000000000000000000000000

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