Finite Group Databasebeta

← Group #166278

Character table — Group #166278

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444444444442444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1111-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-11-111-1111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-11-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-111-1-11111-1-111-1-111-1-111-1-111-1-111-11-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-11111-1-111-1-111-1-111-1-111-1-1-1-1-1111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111-111111-1-1-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111-1111-1-1-1-11111-1-1-1-11111-1-1
χ1311111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-11-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-11-11-1111-1-1-111-1-1-1-111-1-111
χ1611111111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-11-11-1-1-11-111-1-11111-1-111-1-1
χ172222222222222-2-2-2-2-22-22-200002222000000-20000-200000000000000
χ182222222222222-2-2-2-2-22-22-20000-2-2-2-200000020000200000000000000
χ19222222222222-22-2-2-2-2-22-222222000000000-20000-2000000000000000
χ20222222222222-22-2-2-2-2-22-22-2-2-2-2000000000200002000000000000000
χ21222222222222-2-22222-2-2-2-2000000002222-200-2000000000000000000
χ22222222222222-2-22222-2-2-2-200000000-2-2-2-22002000000000000000000
χ2322222222-2-2-2-22-222-2-22-2-22000022-2-200000020000-200000000000000
χ2422222222-2-2-2-22-222-2-22-2-220000-2-222000000-20000200000000000000
χ2522222222-2-2-2-2-2222-2-2-222-222-2-2000000000-200002000000000000000
χ2622222222-2-2-2-2-2222-2-2-222-2-2-22200000000020000-2000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2220000000022-2-2-2002000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-2-222200-2000000000000000000
χ29222-2-2-2-222i2i−2i−2i002i−2i2-20000000000002i−2i2-2000000000000002−2i2−i2i2−i22−2
χ30222-2-2-2-222i2i−2i−2i002i−2i2-20000000000002i−2i2-200000000000000−22−i2i2−i2i2−22
χ31222-2-2-2-222i2i−2i−2i002i−2i2-2000000000000−2i2i-22000000000000002−2i2−i2−i2i2−22
χ32222-2-2-2-222i2i−2i−2i002i−2i2-2000000000000−2i2i-2200000000000000−22−i2i2i2−i22−2
χ33222-2-2-2-22−2i−2i2i2i00−2i2i2-20000000000002i−2i-22000000000000002−2−i2i2i2−i2−22
χ34222-2-2-2-22−2i−2i2i2i00−2i2i2-20000000000002i−2i-2200000000000000−22i2−i2−i2i22−2
χ35222-2-2-2-22−2i−2i2i2i00−2i2i2-2000000000000−2i2i2-2000000000000002−2−i2i2−i2i22−2
χ36222-2-2-2-22−2i−2i2i2i00−2i2i2-2000000000000−2i2i2-200000000000000−22i2−i2i2−i2−22
χ37444-4-4-4-444i4i−4i−4i00−4i4i-4400000000000000000000000000000000000000
χ38444-4-4-4-44−4i−4i4i4i004i−4i-4400000000000000000000000000000000000000
χ3944-44-44-4-400000400000-400004-4000000000000000000000000000000
χ4044-44-44-4-400000400000-40000-44000000000000000000000000000000
χ4144-44-44-4-400000-4000004004i−4i00000000000000000000000000000000
χ4244-44-44-4-400000-400000400−4i4i00000000000000000000000000000000
χ434-44-444-4-40000400000-400000004-40000000000000000000000000000
χ444-44-444-4-40000400000-40000000-440000000000000000000000000000
χ454-44-444-4-40000-40000040000000004i−4i00000000000000000000000000
χ464-44-444-4-40000-4000004000000000−4i4i00000000000000000000000000
χ474-4-444-4-444i−4i4i−4i000000000000000000000000002i−2i002-2000000000000
χ484-4-444-4-444i−4i4i−4i00000000000000000000000000−2i2i00-22000000000000
χ494-4-444-4-44−4i4i−4i4i000000000000000000000000002i−2i00-22000000000000
χ504-4-444-4-44−4i4i−4i4i00000000000000000000000000−2i2i002-2000000000000
χ514-4-4-4-44444-4-44000000000000000000000000000000002-22-200000000
χ524-4-4-4-44444-4-4400000000000000000000000000000000-22-2200000000
χ534-4-4-4-4444-444-4000000000000000000000000000000002-2-2200000000
χ544-4-4-4-4444-444-400000000000000000000000000000000-222-200000000
χ5588-8-88-88-8000000000000000000000000000000000000000000000000
χ568-888-8-88-8000000000000000000000000000000000000000000000000

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