Finite Group Databasebeta

← Group #100769

Character table — Group #100769

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111111122224444448881616161616161616161616161616161616161616161616163232
order12222222444444444444424448888888888888888888844
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
χ5111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-11-1-1111-111-1-1i−ii−ii−ii−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-1-1-11-1-1111-111-1-1i−ii−ii−ii−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-1-1-11-1-1111-111-1-1−ii−ii−ii−iiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-1-1-11-1-1111-111-1-1−ii−ii−ii−ii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-1-1-11-1-1111-1-1-111i−i−iii−i−iiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-1-1-11-1-1111-1-1-111i−i−iii−i−ii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-1-1-11-1-1111-1-1-111−iii−i−iii−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-1-1-11-1-1111-1-1-111−iii−i−iii−i−i−iiiii−i−i11-1-1-11
χ172222222222222-2-22-2-22-2-20000002200-2-200000000000000
χ182222222222222-2-22-2-22-2-2000000-2-2002200000000000000
χ19222222222222-22-2-22-2-22-200002200-2-20000000000000000
χ20222222222222-22-2-22-2-22-20000-2-200220000000000000000
χ21222222222222-2-22-2-22-2-222-22-20000000000000000000000
χ22222222222222-2-22-2-22-2-22-22-220000000000000000000000
χ2322222222-2-2-2-2222222-2-2-22-2-220000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-222-20000000000000000000000
χ2522222222-2-2-2-22-2-22-2-2-22200002i−2i00−2i2i0000000000000000
χ2622222222-2-2-2-22-2-22-2-2-2220000−2i2i002i−2i0000000000000000
χ2722222222-2-2-2-2-22-2-22-22-220000002i−2i00−2i2i00000000000000
χ2822222222-2-2-2-2-22-2-22-22-22000000−2i2i002i−2i00000000000000
χ29444-4-44-4-444-4-40000000000000000000002-22-20000000000
χ30444-4-44-4-444-4-4000000000000000000000-22-220000000000
χ31444-4-44-4-4-4-4440000000000000000000002i−2i−2i2i0000000000
χ32444-4-44-4-4-4-444000000000000000000000−2i2i2i−2i0000000000
χ3344-44-4-4-440000444-4-4-400000000000000000000000000000
χ3444-44-4-4-4400004-4-4-44400000000000000000000000000000
χ3544-44-4-4-440000-44-44-4400000000000000000000000000000
χ3644-44-4-4-440000-4-4444-400000000000000000000000000000
χ374-4-4444-4-44-44-400000000000000000000000002-22-2000000
χ384-4-4444-4-44-44-40000000000000000000000000-22-22000000
χ394-4-4444-4-4-44-4400000000000000000000000002i−2i−2i2i000000
χ404-4-4444-4-4-44-440000000000000000000000000−2i2i2i−2i000000
χ414-4-4-4-44444-4-44000000000000000000000000000002-22-200
χ424-4-4-4-44444-4-4400000000000000000000000000000-22-2200
χ434-4-4-4-4444-444-4000000000000000000000000000002-2-2200
χ444-4-4-4-4444-444-400000000000000000000000000000-222-200
χ4588-8-88-88-8000000000000000000000000000000000000000
χ468-888-8-88-8000000000000000000000000000000000000000
χ478-88-88-8-88000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).