Finite Group Databasebeta

← Group #97036

Character table — Group #97036

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-2-222-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000
χ2122222222-2-2-2-222-2-222-2-222-2-200000000002-2002-20000000000000000
χ2222222222-2-2-2-222-2-222-2-222-2-20000000000-2200-220000000000000000
χ2322222222-2-2-2-222-2-2-2-222-2-22200000000002-200-220000000000000000
χ2422222222-2-2-2-222-2-2-2-222-2-2220000000000-22002-20000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-222000000002-2002-2000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-22200000000-2200-22000000000000000000
χ2722222222-2-2-2-2-2-222-2-22222-2-2000000002-200-22000000000000000000
χ2822222222-2-2-2-2-2-222-2-22222-2-200000000-22002-2000000000000000000
χ2922-2-2-222-222-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3022-2-2-222-222-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3122-2-2-222-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3222-2-2-222-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3322-2-2-222-222-2-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3422-2-2-222-222-2-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3522-2-2-222-222-2-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3622-2-2-222-222-2-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ3722-2-2-222-2-2-2222-2-222i−2i−2i2i2i−2i−2i2i00000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ3822-2-2-222-2-2-2222-2-222i−2i−2i2i2i−2i−2i2i0000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ3922-2-2-222-2-2-2222-2-22−2i2i2i−2i−2i2i2i−2i00000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ4022-2-2-222-2-2-2222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ4122-2-2-222-2-2-222-222-22i−2i−2i2i−2i2i2i−2i000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4222-2-2-222-2-2-222-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4322-2-2-222-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4422-2-2-222-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ454444-4-4-4-44-44-4000000000000004-40000000000000000000000000000
χ464444-4-4-4-44-44-400000000000000-440000000000000000000000000000
χ474444-4-4-4-4-44-440000000000004-4000000000000000000000000000000
χ484444-4-4-4-4-44-44000000000000-44000000000000000000000000000000
χ4944-4-44-4-444-4-4400000000000000004i−4i00000000000000000000000000
χ5044-4-44-4-444-4-440000000000000000−4i4i00000000000000000000000000
χ5144-4-44-4-44-444-40000000000000000004i−4i000000000000000000000000
χ5244-4-44-4-44-444-4000000000000000000−4i4i000000000000000000000000
χ538-88-888-8-8000000000000000000000000000000000000000000000000
χ548-88-8-8-888000000000000000000000000000000000000000000000000
χ558-8-888-88-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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