Finite Group Databasebeta

← Group #166157

Character table — Group #166157

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444222444444444442244444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ6111111111111111111111-1-1-1-1111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ911111111-1-1-1-11-1-111111-111-1-1-11111-1-1-1-1111-11-11-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-111111-111-1-1-11111-1-1-1-1-1-11-11-11-111-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-111111-111-1-1-1-1-1-1-1111111-111-1-11-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-111111-111-1-1-1-1-1-1-11111-1-1-111-1-1111-1-11111-1-111-1-1
χ1311111111-1-1-1-11-1-111111-1-1-111-111-1-1-1-111111-1-11-11-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-11-1-111111-1-1-111-111-1-1-1-111-1-11-1-11-111111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-111111-1-1-111-1-1-11111-1-111-11-111-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-11-1-111111-1-1-111-1-1-11111-1-1-1-1-11-111-11111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-22-2000022200220000-2-2000000000000000000
χ182222222222222-2-2-2-2-2-22-200002-2-200-2-2000022000000000000000000
χ19222222222222-222-2-222-2-22222-2000000000000-2-20000000000000000
χ20222222222222-222-2-222-2-2-2-2-2-2-2000000000000220000000000000000
χ21222222222222-2-2-222-2-2-220000-200220022000000-2-200000000000000
χ22222222222222-2-2-222-2-2-220000-200-2-200-2-20000002200000000000000
χ2322222222-2-2-2-2222-2-2-2-2220000-22200-2-20000-22000000000000000000
χ2422222222-2-2-2-2222-2-2-2-2220000-2-2-2002200002-2000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-200002002200-2-2000000-2200000000000000
χ2622222222-2-2-2-2-22222-2-2-2-20000200-2-200220000002-200000000000000
χ2722222222-2-2-2-2-2-2-2-2-222-2222-2-22000000000000-220000000000000000
χ2822222222-2-2-2-2-2-2-2-2-222-22-2-22220000000000002-20000000000000000
χ2922-22-2-22-22i2i−2i−2i02i−2i002-2002-22i−2i000000000000000000000002−2i2−i22−2i2−i2
χ3022-22-2-22-22i2i−2i−2i02i−2i002-2002-22i−2i00000000000000000000000−22−i2i2−22−i2i2
χ3122-22-2-22-22i2i−2i−2i02i−2i002-200-22−2i2i000000000000000000000002−2i2−i2−22−i2i2
χ3222-22-2-22-22i2i−2i−2i02i−2i002-200-22−2i2i00000000000000000000000−22−i2i22−2i2−i2
χ3322-22-2-22-2−2i−2i2i2i0−2i2i002-2002-2−2i2i000000000000000000000002−2−i2i22−2−i2i2
χ3422-22-2-22-2−2i−2i2i2i0−2i2i002-2002-2−2i2i00000000000000000000000−22i2−i2−22i2−i2
χ3522-22-2-22-2−2i−2i2i2i0−2i2i002-200-222i−2i000000000000000000000002−2−i2i2−22i2−i2
χ3622-22-2-22-2−2i−2i2i2i0−2i2i002-200-222i−2i00000000000000000000000−22i2−i22−2−i2i2
χ3744-44-4-44-44i4i−4i−4i0−4i4i00-440000000000000000000000000000000000000
χ3844-44-4-44-4−4i−4i4i4i04i−4i00-440000000000000000000000000000000000000
χ3944-4-44-4-4400004000000-40000004i−4i0000000000000000000000000000
χ4044-4-44-4-4400004000000-4000000−4i4i0000000000000000000000000000
χ4144-4-44-4-440000-4000000400000000004-4000000000000000000000000
χ4244-4-44-4-440000-400000040000000000-44000000000000000000000000
χ434-44-44-44-44i−4i4i−4i000000000000000000000000000000002-22i−2i00000000
χ444-44-44-44-44i−4i4i−4i00000000000000000000000000000000-22−2i2i00000000
χ454-44-44-44-4−4i4i−4i4i000000000000000000000000000000002-2−2i2i00000000
χ464-44-44-44-4−4i4i−4i4i00000000000000000000000000000000-222i−2i00000000
χ474-4-4444-4-400000004-40000000000000004i−4i0000000000000000000000
χ484-4-4444-4-400000004-4000000000000000−4i4i0000000000000000000000
χ494-4-4444-4-40000000-44000000000004i−4i00000000000000000000000000
χ504-4-4444-4-40000000-4400000000000−4i4i00000000000000000000000000
χ514-4-4-4-44444-4-4400000000000000000000002-20000002-2000000000000
χ524-4-4-4-44444-4-440000000000000000000000-22000000-22000000000000
χ534-4-4-4-4444-444-400000000000000000000002-2000000-22000000000000
χ544-4-4-4-4444-444-40000000000000000000000-220000002-2000000000000
χ55888-8-88-8-8000000000000000000000000000000000000000000000000
χ568-888-8-8-88000000000000000000000000000000000000000000000000

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