Finite Group Databasebeta

← Group #100740

Character table — Group #100740

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111111122224444448881616161616161616161616161616161616161616161616163232
order12222222444444444444444448888888888888888888824
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-111-1-11-1111-1-1i−ii−iii−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-1-1-111-1-11-1111-1-1i−ii−iii−i−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-1-1-111-1-11-1111-1-1−ii−ii−i−iiiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-1-1-111-1-11-1111-1-1−ii−ii−i−iii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-1-1-111-1-11-11-1-111i−ii−i−i−iiiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-1-1-111-1-11-11-1-111i−ii−i−i−iii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-1-1-111-1-11-11-1-111−ii−iiii−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-1-1-111-1-11-11-1-111−ii−iiii−i−i−i−iiiii−i−i11-1-1-11
χ1722222222222222-2-2-2-22-2-2000022-2-2000000000000000000
χ1822222222222222-2-2-2-22-2-20000-2-222000000000000000000
χ19222222222222-2-222-2-2-22-22-22-20000000000000000000000
χ20222222222222-2-222-2-2-22-2-22-220000000000000000000000
χ21222222222222-2-2-2-222-2-22000000002-22-200000000000000
χ22222222222222-2-2-2-222-2-2200000000-22-2200000000000000
χ2322222222-2-2-2-2222222-2-2-22-2-220000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-222-20000000000000000000000
χ2522222222-2-2-2-222-2-2-2-2-222000000002i−2i−2i2i00000000000000
χ2622222222-2-2-2-222-2-2-2-2-22200000000−2i2i2i−2i00000000000000
χ2722222222-2-2-2-2-2-2-2-22222-200002i−2i−2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-20000−2i2i2i−2i000000000000000000
χ2944-4-444-4-400004i−4i4-44i−4i00000000000000000000000000000
χ3044-4-444-4-400004i−4i-44−4i4i00000000000000000000000000000
χ3144-4-444-4-40000−4i4i4-4−4i4i00000000000000000000000000000
χ3244-4-444-4-40000−4i4i-444i−4i00000000000000000000000000000
χ3344-4-4-4-44444-4-40000000000000000000002i−2i2i−2i0000000000
χ3444-4-4-4-44444-4-4000000000000000000000−2i2i−2i2i0000000000
χ3544-4-4-4-444-4-4440000000000000000000002-2-220000000000
χ3644-4-4-4-444-4-444000000000000000000000-222-20000000000
χ374-44-44-44-44i−4i4i−4i000000000000000000000000000002-22i−2i00
χ384-44-44-44-44i−4i4i−4i00000000000000000000000000000-22−2i2i00
χ394-44-44-44-4−4i4i−4i4i000000000000000000000000000002-2−2i2i00
χ404-44-44-44-4−4i4i−4i4i00000000000000000000000000000-222i−2i00
χ414-4-44-444-44i−4i−4i4i00000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ424-4-44-444-44i−4i−4i4i0000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ434-4-44-444-4−4i4i4i−4i00000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ444-4-44-444-4−4i4i4i−4i0000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ458888-8-8-8-8000000000000000000000000000000000000000
χ468-88-8-88-88000000000000000000000000000000000000000
χ478-8-888-8-88000000000000000000000000000000000000000

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