Finite Group Databasebeta

← Group #166248

Character table — Group #166248

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444224444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-111-1-1-1-1-1-11111-1-11-1-111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-111-1-1-1-1-1-11111-1-11-1-11-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11-1-11111111-1-1-1-111-1-111-1-11-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-11111111-1-1-1-111-1-111-1-11-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11111111-1-1-1-1-1-111-1-111-11-11-1111-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-11-1-11111111-1-1-1-1-1-111-1-111-11-11-11-1-11111-1-1-1-11111-1-1
χ1311111111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1111-1-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1111-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-111-11-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-111-11-1-1-11111-1-111-1-1-1-111
χ172222222222222-2-2-2-2-22-2002-2000000222200-200-20000000000000000
χ182222222222222-2-2-2-2-22-2002-2000000-2-2-2-20020020000000000000000
χ19222222222222-222-222-2-200-2-20022220000-2-200000000000000000000
χ20222222222222-222-222-2-200-2-200-2-2-2-200002200000000000000000000
χ21222222222222-2-2-22-2-2-2222-222200000000000-2-200000000000000000
χ22222222222222-2-2-22-2-2-22-2-2-22-2-2000000000002200000000000000000
χ2322222222-2-2-2-2222-2-2-22-200-2200000022-2-200-20020000000000000000
χ2422222222-2-2-2-2222-2-2-22-200-22000000-2-22200200-20000000000000000
χ2522222222-2-2-2-2-2222-2-2-22222-2-2-200000000000-2200000000000000000
χ2622222222-2-2-2-2-2222-2-2-22-2-22-222000000000002-200000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-200220022-2-20000-2200000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2002200-2-22200002-200000000000000000000
χ2922-2-222-2-22i2i−2i−2i02i−2i02-2000000002i−2i2-20000000000000000002−2i2−i2i2−i22−2
χ3022-2-222-2-22i2i−2i−2i02i−2i02-2000000002i−2i2-2000000000000000000−22−i2i2−i2i2−22
χ3122-2-222-2-22i2i−2i−2i02i−2i02-200000000−2i2i-220000000000000000002−2i2−i2−i2i2−22
χ3222-2-222-2-22i2i−2i−2i02i−2i02-200000000−2i2i-22000000000000000000−22−i2i2i2−i22−2
χ3322-2-222-2-2−2i−2i2i2i0−2i2i02-2000000002i−2i-220000000000000000002−2−i2i2i2−i2−22
χ3422-2-222-2-2−2i−2i2i2i0−2i2i02-2000000002i−2i-22000000000000000000−22i2−i2−i2i22−2
χ3522-2-222-2-2−2i−2i2i2i0−2i2i02-200000000−2i2i2-20000000000000000002−2−i2i2−i2i22−2
χ3622-2-222-2-2−2i−2i2i2i0−2i2i02-200000000−2i2i2-2000000000000000000−22i2−i2i2−i2−22
χ37444-4-4-44-400000004000-44-40000000000000000000000000000000000
χ38444-4-4-44-400000004000-4-440000000000000000000000000000000000
χ39444-4-4-44-40000000-4000400004i−4i000000000000000000000000000000
χ40444-4-4-44-40000000-400040000−4i4i000000000000000000000000000000
χ4144-4-444-4-44i4i−4i−4i0−4i4i0-4400000000000000000000000000000000000000
χ4244-4-444-4-4−4i−4i4i4i04i−4i0-4400000000000000000000000000000000000000
χ434-4444-4-4-40000400000-400000000000004-40000000000000000000000
χ444-4444-4-4-40000400000-40000000000000-440000000000000000000000
χ454-4444-4-4-40000-4000004000000000004i−4i000000000000000000000000
χ464-4444-4-4-40000-400000400000000000−4i4i000000000000000000000000
χ474-44-4-44-444-44-4000000000000000000000000000000002i−2i2i−2i00000000
χ484-44-4-44-444-44-400000000000000000000000000000000−2i2i−2i2i00000000
χ494-44-4-44-44-44-44000000000000000000000000000000002i−2i−2i2i00000000
χ504-44-4-44-44-44-4400000000000000000000000000000000−2i2i2i−2i00000000
χ514-4-44-444-44i−4i−4i4i00000000000000000000000000002-22i−2i000000000000
χ524-4-44-444-44i−4i−4i4i0000000000000000000000000000-22−2i2i000000000000
χ534-4-44-444-4−4i4i4i−4i00000000000000000000000000002-2−2i2i000000000000
χ544-4-44-444-4−4i4i4i−4i0000000000000000000000000000-222i−2i000000000000
χ5588-88-8-8-88000000000000000000000000000000000000000000000000
χ568-8-8-88-888000000000000000000000000000000000000000000000000

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