Finite Group Databasebeta

← Group #166232

Character table — Group #166232

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444224444444444442444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-11111-1-1-1-11-11-1-11-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-11111-1-1-1-11-11-1-11-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1-1-111111-1-11-1-111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-111111-1-11-1-11-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-11-11-1111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-11-11-11-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1-1111-111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1-1111-1-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-111-1111-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-111-1111-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-11-1-1-11111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-11-1-1-111-1-11111-1-111-1-1-1-111
χ1722222222222222-2-222-2-222-22200000000-2-200-2000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-200000000-22002000000000000000000
χ19222222222222-2-222-2-2-2-200-20000002222200-200-20000000000000000
χ20222222222222-2-222-2-2-2-200-2000000-2-2-2-220020020000000000000000
χ21222222222222-2-2-2-2-2-2220020022220000-20-200-200000000000000000
χ22222222222222-2-2-2-2-2-22200200-2-2-2-20000-20200200000000000000000
χ2322222222-2-2-2-22222-2-2-2-200200000022-2-2-200200-20000000000000000
χ2422222222-2-2-2-22222-2-2-2-2002000000-2-222-200-20020000000000000000
χ2522222222-2-2-2-222-2-2-2-22200-20022-2-2000020-200200000000000000000
χ2622222222-2-2-2-222-2-2-2-22200-200-2-222000020200-200000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2222-2-2000000002200-2000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-2222000000002-2002000000000000000000
χ2922-22-2-22-22i2i−2i−2i2i−2i002-2002-202i−2i000000000000000000000002−2i2−i22−2i2−i2
χ3022-22-2-22-22i2i−2i−2i2i−2i002-2002-202i−2i00000000000000000000000−22−i2i2−22−i2i2
χ3122-22-2-22-22i2i−2i−2i2i−2i002-200-220−2i2i000000000000000000000002−2i2−i2−22−i2i2
χ3222-22-2-22-22i2i−2i−2i2i−2i002-200-220−2i2i00000000000000000000000−22−i2i22−2i2−i2
χ3322-22-2-22-2−2i−2i2i2i−2i2i002-2002-20−2i2i000000000000000000000002−2−i2i22−2−i2i2
χ3422-22-2-22-2−2i−2i2i2i−2i2i002-2002-20−2i2i00000000000000000000000−22i2−i2−22i2−i2
χ3522-22-2-22-2−2i−2i2i2i−2i2i002-200-2202i−2i000000000000000000000002−2−i2i2−22i2−i2
χ3622-22-2-22-2−2i−2i2i2i−2i2i002-200-2202i−2i00000000000000000000000−22i2−i22−2−i2i2
χ3744-44-4-44-44i4i−4i−4i−4i4i00-4400000000000000000000000000000000000000
χ3844-44-4-44-4−4i−4i4i4i4i−4i00-4400000000000000000000000000000000000000
χ3944-4-44-4-4400000000004-400000004i−4i000000000000000000000000000
χ4044-4-44-4-4400000000004-40000000−4i4i000000000000000000000000000
χ4144-4-44-4-440000000000-44000004i−4i00000000000000000000000000000
χ4244-4-44-4-440000000000-4400000−4i4i00000000000000000000000000000
χ434-444-4-4-444i−4i4i−4i00000000000000000000000000002i−2i2-2000000000000
χ444-444-4-4-444i−4i4i−4i0000000000000000000000000000−2i2i-22000000000000
χ454-444-4-4-44−4i4i−4i4i00000000000000000000000000002i−2i-22000000000000
χ464-444-4-4-44−4i4i−4i4i0000000000000000000000000000−2i2i2-2000000000000
χ474-44-44-44-40000004-40000000000000004i−4i00000000000000000000000
χ484-44-44-44-40000004-4000000000000000−4i4i00000000000000000000000
χ494-44-44-44-4000000-4400000000000004i−4i0000000000000000000000000
χ504-44-44-44-4000000-440000000000000−4i4i0000000000000000000000000
χ514-4-4444-4-44-4-44000000000000000000000000000000002i−2i2i−2i00000000
χ524-4-4444-4-44-4-4400000000000000000000000000000000−2i2i−2i2i00000000
χ534-4-4444-4-4-444-4000000000000000000000000000000002i−2i−2i2i00000000
χ544-4-4444-4-4-444-400000000000000000000000000000000−2i2i2i−2i00000000
χ55888-8-88-8-8000000000000000000000000000000000000000000000000
χ568-8-8-8-8888000000000000000000000000000000000000000000000000

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