Finite Group Databasebeta

← Group #134342

Character table — Group #134342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222-2-2222222-2-222-2-20000-2-2000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-2-2-222-2-2-2-222000022000000000000000000000000
χ19222222222222-2-2-2-2-2-2222222-2-222-2-2220000-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2000022000000000000000000000000
χ21222-2-2-2-222-22-222-2-22i−2i2i−2i00002i−2i2i−2i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ22222-2-2-2-222-22-222-2-22i−2i2i−2i00002i−2i2i−2i000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ23222-2-2-2-222-22-222-2-2−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ24222-2-2-2-222-22-222-2-2−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ25222-2-2-2-222-22-2-2-2222i−2i−2i2i00002i−2i−2i2i000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ26222-2-2-2-222-22-2-2-2222i−2i−2i2i00002i−2i−2i2i00000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ27222-2-2-2-222-22-2-2-222−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ28222-2-2-2-222-22-2-2-222−2i2i2i−2i0000−2i2i2i−2i00000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ2922-222-2-2-2-2-2222-22-22i−2i2i−2i0000−2i2i−2i2i00000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ3022-222-2-2-2-2-2222-22-22i−2i2i−2i0000−2i2i−2i2i0000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ3122-222-2-2-2-2-2222-22-2−2i2i−2i2i00002i−2i2i−2i00000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ3222-222-2-2-2-2-2222-22-2−2i2i−2i2i00002i−2i2i−2i0000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ3322-222-2-2-2-2-222-22-222i−2i−2i2i0000−2i2i2i−2i0000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ3422-222-2-2-2-2-222-22-222i−2i−2i2i0000−2i2i2i−2i000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ3522-222-2-2-2-2-222-22-22−2i2i2i−2i00002i−2i−2i2i0000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ3622-222-2-2-2-2-222-22-22−2i2i2i−2i00002i−2i−2i2i000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ3722-2-2-222-2-222-22-2-2222220000-2-2-2-2000022-2-20000002-2000000000000000000
χ3822-2-2-222-2-222-22-2-2222220000-2-2-2-20000-2-222000000-22000000000000000000
χ3922-2-2-222-2-222-22-2-22-2-2-2-200002222000022-2-2000000-22000000000000000000
χ4022-2-2-222-2-222-22-2-22-2-2-2-2000022220000-2-2220000002-2000000000000000000
χ4122-2-2-222-2-222-2-222-222-2-20000-2-22200000000002i2i−2i−2i002i−2i0000000000000000
χ4222-2-2-222-2-222-2-222-222-2-20000-2-2220000000000−2i−2i2i2i00−2i2i0000000000000000
χ4322-2-2-222-2-222-2-222-2-2-222000022-2-200000000002i2i−2i−2i00−2i2i0000000000000000
χ4422-2-2-222-2-222-2-222-2-2-222000022-2-20000000000−2i−2i2i2i002i−2i0000000000000000
χ4544444444-4-4-4-40000000044-4-400000000000000000000000000000000000000
χ4644444444-4-4-4-400000000-4-44400000000000000000000000000000000000000
χ47444-4-4-4-44-44-440000000000000000004i−4i000000000000000000000000000000
χ48444-4-4-4-44-44-44000000000000000000−4i4i000000000000000000000000000000
χ4944-444-4-4-444-4-400000000000000004-400000000000000000000000000000000
χ5044-444-4-4-444-4-40000000000000000-4400000000000000000000000000000000
χ5144-4-4-444-44-4-440000000000000000000000004i−4i000000000000000000000000
χ5244-4-4-444-44-4-44000000000000000000000000−4i4i000000000000000000000000
χ534-444-4-44-4000000000000004i−4i000000002-22-2002i−2i2i−2i00000000000000000000
χ544-444-4-44-4000000000000004i−4i00000000-22-2200−2i2i−2i2i00000000000000000000
χ554-444-4-44-400000000000000−4i4i000000002-22-200−2i2i−2i2i00000000000000000000
χ564-444-4-44-400000000000000−4i4i00000000-22-22002i−2i2i−2i00000000000000000000
χ574-4-4-44-4440000000000004-400000000002-2-22002-2-2200000000000000000000
χ584-4-4-44-4440000000000004-40000000000-222-200-222-200000000000000000000
χ594-4-4-44-444000000000000-4400000000002-2-2200-222-200000000000000000000
χ604-4-4-44-444000000000000-440000000000-222-2002-2-2200000000000000000000
χ618-88-888-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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