Finite Group Databasebeta

← Group #166222

Character table — Group #166222

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444224444444444442444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11111-1-1-1-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-111-1-111-1-1-1-111-1-1-111-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-111-1-111-1-1-1-111-1-1-111-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-11-11-1111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-11-11-11-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-11111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-11-111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-11-1-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11-111-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11-111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222-2-2-2-22222-2-20000220000-20000-20000000000000000
χ1822222222222222-2-2-2-222-2-2-2-20000-2-200002000020000000000000000
χ19222222222222-2-222-2-2-2-2002-20022000022000-2-200000000000000000
χ20222222222222-2-222-2-2-2-2002-200-2-20000-2-20002200000000000000000
χ21222222222222-2-2-2-222-2-200-2222000022000-2-20000000000000000000
χ22222222222222-2-2-2-222-2-200-22-2-20000-2-2000220000000000000000000
χ2322222222-2-2-2-22222-2-2-2-200-2200220000-2-2000-2200000000000000000
χ2422222222-2-2-2-22222-2-2-2-200-2200-2-20000220002-200000000000000000
χ2522222222-2-2-2-222-2-222-2-2002-2220000-2-2000-220000000000000000000
χ2622222222-2-2-2-222-2-222-2-2002-2-2-20000220002-20000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222220000-2-2000020000-20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2220000220000-2000020000000000000000
χ29222-2-2-22-22i2i−2i−2i2i−2i00002-22-20000002i−2i000000000000000000i2−i22−2i2−i22−2
χ30222-2-2-22-22i2i−2i−2i2i−2i00002-22-20000002i−2i000000000000000000−i2i2−22−i2i2−22
χ31222-2-2-22-22i2i−2i−2i2i−2i00002-2-22000000−2i2i000000000000000000i2−i22−2−i2i2−22
χ32222-2-2-22-22i2i−2i−2i2i−2i00002-2-22000000−2i2i000000000000000000−i2i2−22i2−i22−2
χ33222-2-2-22-2−2i−2i2i2i−2i2i00002-22-2000000−2i2i000000000000000000i2−i2−22i2−i2−22
χ34222-2-2-22-2−2i−2i2i2i−2i2i00002-22-2000000−2i2i000000000000000000−i2i22−2−i2i22−2
χ35222-2-2-22-2−2i−2i2i2i−2i2i00002-2-220000002i−2i000000000000000000i2−i2−22−i2i22−2
χ36222-2-2-22-2−2i−2i2i2i−2i2i00002-2-220000002i−2i000000000000000000−i2i22−2i2−i2−22
χ37444-4-4-44-44i4i−4i−4i−4i4i0000-44000000000000000000000000000000000000
χ38444-4-4-44-4−4i−4i4i4i4i−4i0000-44000000000000000000000000000000000000
χ3944-44-4-4-44000000004-40000000000004i−4i000000000000000000000000
χ4044-44-4-4-44000000004-4000000000000−4i4i000000000000000000000000
χ4144-44-4-4-4400000000-440000004i−4i000000000000000000000000000000
χ4244-44-4-4-4400000000-44000000−4i4i000000000000000000000000000000
χ434-44-44-4-440000004-400000000000000004i−4i0000000000000000000000
χ444-44-44-4-440000004-40000000000000000−4i4i0000000000000000000000
χ454-44-44-4-44000000-4400000000004i−4i0000000000000000000000000000
χ464-44-44-4-44000000-440000000000−4i4i0000000000000000000000000000
χ474-4-444-44-44i−4i4i−4i00000000000000000000000000002-22i−2i000000000000
χ484-4-444-44-44i−4i4i−4i0000000000000000000000000000-22−2i2i000000000000
χ494-4-444-44-4−4i4i−4i4i00000000000000000000000000002-2−2i2i000000000000
χ504-4-444-44-4−4i4i−4i4i0000000000000000000000000000-222i−2i000000000000
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
χ5588-8-888-8-8000000000000000000000000000000000000000000000000
χ568-888-88-8-8000000000000000000000000000000000000000000000000

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