Finite Group Databasebeta

← Group #100875

Character table — Group #100875

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111122224444448888888888888881616161616161616161616161616161616163232
order12222222444444444444444448888888824888888888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-11-1-1111-111-1-1ii−i−iii−i−i-11i−ii−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-1-1-11-1-1111-111-1-1ii−i−iii−i−i-11i−ii−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-1-1-11-1-1111-111-1-1−i−iii−i−iii-11−ii−iiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-1-1-11-1-1111-111-1-1−i−iii−i−iii-11−ii−ii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-1-1-11-1-1111-1-1-111ii−i−i−i−iii1-1i−i−iiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-1-1-11-1-1111-1-1-111ii−i−i−i−iii1-1i−i−ii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-1-1-11-1-1111-1-1-111−i−iiiii−i−i1-1−iii−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-1-1-11-1-1111-1-1-111−i−iiiii−i−i1-1−iii−i−i−iiiii−i−i11-1-1-11
χ172222222222222-2-22-2-22-2-20000000022220000-2-200000000000000
χ182222222222222-2-22-2-22-2-200000000-2-2-2-200002200000000000000
χ19222222222222-22-2-22-2-22-200002222000000-2-20000000000000000
χ20222222222222-22-2-22-2-22-20000-2-2-2-2000000220000000000000000
χ21222222222222-2-22-2-22-2-22222200000000-2-2000000000000000000
χ22222222222222-2-22-2-22-2-22-2-2-2-20000000022000000000000000000
χ2322222222-2-2-2-2222222-2-2-222-2-2000000002-2000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-2-22200000000-22000000000000000000
χ2522222222-2-2-2-22-2-22-2-2-22200002i2i−2i−2i000000−2i2i0000000000000000
χ2622222222-2-2-2-22-2-22-2-2-2220000−2i−2i2i2i0000002i−2i0000000000000000
χ2722222222-2-2-2-2-22-2-22-22-22000000002i2i−2i−2i0000−2i2i00000000000000
χ2822222222-2-2-2-2-22-2-22-22-2200000000−2i−2i2i2i00002i−2i00000000000000
χ29444-4-44-4-400000400-40000000022−2222−22000000000000000000000000
χ30444-4-44-4-400000400-400000000−2222−2222000000000000000000000000
χ31444-4-44-4-400000-4004000000002i2−2i2−2i22i2000000000000000000000000
χ32444-4-44-4-400000-400400000000−2i22i22i2−2i2000000000000000000000000
χ3344-44-4-44-444-4-40000000000000000000000000002-22-20000000000
χ3444-44-4-44-444-4-4000000000000000000000000000-22-220000000000
χ3544-44-4-44-4-4-4440000000000000000000000000002i−2i−2i2i0000000000
χ3644-44-4-44-4-4-444000000000000000000000000000−2i2i2i−2i0000000000
χ3744-4-44-4-44000000400-40004i−4i000000000000000000000000000000
χ3844-4-44-4-44000000400-4000−4i4i000000000000000000000000000000
χ3944-4-44-4-44000000-4004000004-40000000000000000000000000000
χ4044-4-44-4-44000000-400400000-440000000000000000000000000000
χ414-44-44-44-44-44-400000000000000000000000000000002-22-2000000
χ424-44-44-44-44-44-40000000000000000000000000000000-22-22000000
χ434-44-44-44-4-44-4400000000000000000000000000000002i−2i−2i2i000000
χ444-44-44-44-4-44-440000000000000000000000000000000−2i2i2i−2i000000
χ454-4-4444-4-40000400-4000000000000022−2222−2200000000000000000000
χ464-4-4444-4-40000400-40000000000000−2222−222200000000000000000000
χ474-4-4444-4-40000-400400000000000002i2−2i2−2i22i200000000000000000000
χ484-4-4444-4-40000-40040000000000000−2i22i22i2−2i200000000000000000000
χ494-4-4-4-44444-4-44000000000000000000000000000000000002-22-200
χ504-4-4-4-44444-4-4400000000000000000000000000000000000-22-2200
χ514-4-4-4-4444-444-4000000000000000000000000000000000002-2-2200
χ524-4-4-4-4444-444-400000000000000000000000000000000000-222-200
χ538-888-8-8-88000000000000000000000000000000000000000000000

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