Finite Group Databasebeta

← Group #166102

Character table — Group #166102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444224444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11-11-11-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11-11-11-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1-11-1111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1-11-11-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-111-1-1111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-111-1-11-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-11-111-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-11-111-1-1-11111-1-111-1-1-1-111
χ1722222222222222-2-22-2-2222-2-20000000022-2-200000000000000000000
χ1822222222222222-2-22-2-22-2-2-2-200000000-2-22200000000000000000000
χ19222222222222-2-22-2-22-2-2002-200002222000000-2-20000000000000000
χ20222222222222-2-22-2-22-2-2002-20000-2-2-2-2000000220000000000000000
χ21222222222222-2-2-22-2-22-200-22222200000000-2-2000000000000000000
χ22222222222222-2-2-22-2-22-200-22-2-2-2-20000000022000000000000000000
χ2322222222-2-2-2-2222-2-22-2-200-22000022-2-2000000-220000000000000000
χ2422222222-2-2-2-2222-2-22-2-200-220000-2-2220000002-20000000000000000
χ2522222222-2-2-2-222-22-2-22-2002-222-2-200000000-22000000000000000000
χ2622222222-2-2-2-222-22-2-22-2002-2-2-222000000002-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-22222200000000-2-2-2200000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-22-2-22200000000222-200000000000000000000
χ29222-2-2-2-2222-2-22-200-20022-200000000002-200000000000000i2−i2i2−i2i2−i2i2−i2
χ30222-2-2-2-2222-2-22-200-20022-200000000002-200000000000000−i2i2−i2i2−i2i2−i2i2
χ31222-2-2-2-2222-2-22-200-2002-220000000000-2200000000000000i2−i2i2−i2−i2i2−i2i2
χ32222-2-2-2-2222-2-22-200-2002-220000000000-2200000000000000−i2i2−i2i2i2−i2i2−i2
χ33222-2-2-2-22-2-222-2200-20022-20000000000-2200000000000000i2−i2−i2i2i2−i2−i2i2
χ34222-2-2-2-22-2-222-2200-20022-20000000000-2200000000000000−i2i2i2−i2−i2i2i2−i2
χ35222-2-2-2-22-2-222-2200-2002-2200000000002-200000000000000i2−i2−i2i2−i2i2i2−i2
χ36222-2-2-2-22-2-222-2200-2002-2200000000002-200000000000000−i2i2i2−i2i2−i2−i2i2
χ37444-4-4-4-4444-4-4-4400400-4000000000000000000000000000000000000
χ38444-4-4-4-44-4-4444-400400-4000000000000000000000000000000000000
χ3944-444-4-4-40000000400-400000004-40000000000000000000000000000
χ4044-444-4-4-40000000400-40000000-440000000000000000000000000000
χ4144-444-4-4-40000000-4004000004i−4i000000000000000000000000000000
χ4244-444-4-4-40000000-400400000−4i4i000000000000000000000000000000
χ434-444-44-4-4000000400-40000000000004-4000000000000000000000000
χ444-444-44-4-4000000400-4000000000000-44000000000000000000000000
χ454-444-44-4-4000000-400400000000004i−4i00000000000000000000000000
χ464-444-44-4-4000000-40040000000000−4i4i00000000000000000000000000
χ474-4-44-4-4444-44-4000000000000000000000000000000002-22-200000000
χ484-4-44-4-4444-44-400000000000000000000000000000000-22-2200000000
χ494-4-44-4-444-44-44000000000000000000000000000000002-2-2200000000
χ504-4-44-4-444-44-4400000000000000000000000000000000-222-200000000
χ514-4-4-444-444-4-4400000000000000000000000000002-22-2000000000000
χ524-4-4-444-444-4-440000000000000000000000000000-22-22000000000000
χ534-4-4-444-44-444-400000000000000000000000000002-2-22000000000000
χ544-4-4-444-44-444-40000000000000000000000000000-222-2000000000000
χ5588-8-8-888-8000000000000000000000000000000000000000000000000
χ568-88-88-88-8000000000000000000000000000000000000000000000000

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