Finite Group Databasebeta

← Group #166238

Character table — Group #166238

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444224444444444442444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111-11111-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111111-1-1-1-1-1-11-1-111-1-1111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-11111
χ711111111111111111111-1-111-1-1-1-11111-1-1-1-1-11111-111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-11-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-11-111-111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-11-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111-1111-11-1-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111-11-1-1-11-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-11-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11-1-11-111111-1-111-1-1-1-111
χ1722222222222222-2-222-2-200-2-2000022220000000-2-2000000000000000
χ1822222222222222-2-222-2-200-2-20000-2-2-2-2000000022000000000000000
χ19222222222222-2-222-2-2-2-2002-22222000000-2000000-200000000000000
χ20222222222222-2-222-2-2-2-2002-2-2-2-2-20000002000000200000000000000
χ21222222222222-2-2-2-2-2-22222-2200000000220-2-20000000000000000000
χ22222222222222-2-2-2-2-2-222-2-2-2200000000-2-20220000000000000000000
χ2322222222-2-2-2-22222-2-2-2-200-2222-2-2000000-2000000200000000000000
χ2422222222-2-2-2-22222-2-2-2-200-22-2-2220000002000000-200000000000000
χ2522222222-2-2-2-222-2-2-2-222222-200000000-2-20-220000000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-22-2000000002202-20000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-20022000022-2-20000000-22000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-200220000-2-22200000002-2000000000000000
χ292-22-222-2-22i2i−2i−2i2i−2i002-200000000002-22i−2i0000000000002−2i2−i22−2i2−i20000
χ302-22-222-2-22i2i−2i−2i2i−2i002-200000000002-22i−2i000000000000−22−i2i2−22−i2i20000
χ312-22-222-2-22i2i−2i−2i2i−2i002-20000000000-22−2i2i0000000000002−2i2−i2−22−i2i20000
χ322-22-222-2-22i2i−2i−2i2i−2i002-20000000000-22−2i2i000000000000−22−i2i22−2i2−i20000
χ332-22-222-2-2−2i−2i2i2i−2i2i002-200000000002-2−2i2i0000000000002−2−i2i22−2−i2i20000
χ342-22-222-2-2−2i−2i2i2i−2i2i002-200000000002-2−2i2i000000000000−22i2−i2−22i2−i20000
χ352-22-222-2-2−2i−2i2i2i−2i2i002-20000000000-222i−2i0000000000002−2−i2i2−22i2−i20000
χ362-22-222-2-2−2i−2i2i2i−2i2i002-20000000000-222i−2i000000000000−22i2−i22−2−i2i20000
χ3744-4-44-4-444-44-400000000000000000000000000000000000000002i−2i2i−2i
χ3844-4-44-4-444-44-40000000000000000000000000000000000000000−2i2i−2i2i
χ3944-4-44-4-44-44-4400000000000000000000000000000000000000002i−2i−2i2i
χ4044-4-44-4-44-44-440000000000000000000000000000000000000000−2i2i2i−2i
χ414-444-4-4-440000004-400000000004i−4i0000000000000000000000000000
χ424-444-4-4-440000004-40000000000−4i4i0000000000000000000000000000
χ434-444-4-4-44000000-44000000004i−4i000000000000000000000000000000
χ444-444-4-4-44000000-4400000000−4i4i000000000000000000000000000000
χ454-44-444-4-44i4i−4i−4i−4i4i00-4400000000000000000000000000000000000000
χ464-44-444-4-4−4i−4i4i4i4i−4i00-4400000000000000000000000000000000000000
χ474-4-444-44-44i−4i−4i4i00000000000000000000000002-20002i−2i000000000000
χ484-4-444-44-44i−4i−4i4i0000000000000000000000000-22000−2i2i000000000000
χ494-4-444-44-4−4i4i4i−4i00000000000000000000000002-2000−2i2i000000000000
χ504-4-444-44-4−4i4i4i−4i0000000000000000000000000-220002i−2i000000000000
χ514-4-4-4-444400000000004-40000000000004-40000000000000000000000
χ524-4-4-4-444400000000004-4000000000000-440000000000000000000000
χ534-4-4-4-44440000000000-444-40000000000000000000000000000000000
χ544-4-4-4-44440000000000-44-440000000000000000000000000000000000
χ55888-8-8-88-8000000000000000000000000000000000000000000000000
χ5688-88-88-8-8000000000000000000000000000000000000000000000000

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