Finite Group Databasebeta

← Group #168751

Character table — Group #168751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-11-1-1111111111111-1-1-1-111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ911111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-111-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1111111-1-1-1-11-1-11-1111-1-1-1-111-11
χ1211111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-111-1-1-1-111111-1-11-11-1-11111-1-11-1
χ1311111111-1-1-1-11-1-1-1-111111-1-111-1-1-111-1-1111111-1-1-1-1-111-1-11-1-111-1-1111-1
χ1411111111-1-1-1-11-1-1-1-111111-1-111-1-1-111-1-111-1-1-1-11111-111-1-1111-1-111-1-1-11
χ1511111111-1-1-1-11-1-1-1-111111-1-1-1-111-11111-1-11111-1-1-1-1-11-111-1-1-11111-1-1-11
χ1611111111-1-1-1-11-1-1-1-111111-1-1-1-111-11111-1-1-1-1-1-11111-11-111-111-1-1-1-1111-1
χ172222222222222-2-222-2-2-2-22220000-222000000000000-2-200000000000000
χ182222222222222-2-222-2-2-2-22-2-20000-2-2-20000000000002200000000000000
χ19222222222222-222-2-222-2-2-2000000-2002222000000000000-2-20000000000
χ20222222222222-222-2-222-2-2-2000000-200-2-2-2-2000000000000220000000000
χ21222222222222-2-2-2-2-2-2-222-200222220000000000000000-2-2000000000000
χ22222222222222-2-2-2-2-2-2-222-200-2-2-2-22000000000000000022000000000000
χ2322222222-2-2-2-2222-2-2-2-2-2-222200002-2-2000000000000-2200000000000000
χ2422222222-2-2-2-2222-2-2-2-2-2-22-2-200002220000000000002-200000000000000
χ2522222222-2-2-2-2-22222-2-222-20022-2-2-20000000000000000-22000000000000
χ2622222222-2-2-2-2-22222-2-222-200-2-222-200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-22222-2-2-200000020022-2-2000000000000-220000000000
χ2822222222-2-2-2-2-2-2-22222-2-2-2000000200-2-2220000000000002-20000000000
χ29222-2-22-2-222-2-2-2002-2000022-2000002-20000i2i2−i2−i2i2i2−i2−i2000000i2−i2i2−i2000000
χ30222-2-22-2-222-2-2-2002-2000022-2000002-20000−i2−i2i2i2−i2−i2i2i2000000−i2i2−i2i2000000
χ31222-2-22-2-222-2-2-2002-200002-2200000-220000i2i2−i2−i2i2i2−i2−i2000000−i2i2−i2i2000000
χ32222-2-22-2-222-2-2-2002-200002-2200000-220000−i2−i2i2i2−i2−i2i2i2000000i2−i2i2−i2000000
χ33222-2-22-2-2-2-222-200-22000022-200000-220000i2i2−i2−i2−i2−i2i2i2000000i2−i2−i2i2000000
χ34222-2-22-2-2-2-222-200-22000022-200000-220000−i2−i2i2i2i2i2−i2−i2000000−i2i2i2−i2000000
χ35222-2-22-2-2-2-222-200-2200002-22000002-20000i2i2−i2−i2−i2−i2i2i2000000−i2i2i2−i2000000
χ36222-2-22-2-2-2-222-200-2200002-22000002-20000−i2−i2i2i2i2i2−i2−i2000000i2−i2−i2i2000000
χ372-2-22-222-22i−2i2i−2i02i−2i002-20000000000002i−2i2-2i2−i2i2−i22−22−200000000002−2i2−i200
χ382-2-22-222-22i−2i2i−2i02i−2i002-20000000000002i−2i2-2−i2i2−i2i2−22−220000000000−22−i2i200
χ392-2-22-222-22i−2i2i−2i02i−2i002-2000000000000−2i2i-22i2−i2i2−i22−22−20000000000−22−i2i200
χ402-2-22-222-22i−2i2i−2i02i−2i002-2000000000000−2i2i-22−i2i2−i2i2−22−2200000000002−2i2−i200
χ412-2-22-222-2−2i2i−2i2i0−2i2i002-20000000000002i−2i-22i2−i2i2−i2−22−2200000000002−2−i2i200
χ422-2-22-222-2−2i2i−2i2i0−2i2i002-20000000000002i−2i-22−i2i2−i2i22−22−20000000000−22i2−i200
χ432-2-22-222-2−2i2i−2i2i0−2i2i002-2000000000000−2i2i2-2i2−i2i2−i2−22−220000000000−22i2−i200
χ442-2-22-222-2−2i2i−2i2i0−2i2i002-2000000000000−2i2i2-2−i2i2−i2i22−22−200000000002−2−i2i200
χ45444-4-44-4-444-4-4400-440000-40000000000000000000000000000000000000
χ46444-4-44-4-4-4-4444004-40000-40000000000000000000000000000000000000
χ474-44-4-4-444000000000004-4000004i−4i0000000000000000000000000000000
χ484-44-4-4-444000000000004-400000−4i4i0000000000000000000000000000000
χ494-44-4-4-44400000000000-440004i−4i000000000000000000000000000000000
χ504-44-4-4-44400000000000-44000−4i4i000000000000000000000000000000000
χ514-4-44-444-44i−4i4i−4i0−4i4i00-440000000000000000000000000000000000000000
χ524-4-44-444-4−4i4i−4i4i04i−4i00-440000000000000000000000000000000000000000
χ534-4-4-444-444i−4i−4i4i000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ544-4-4-444-444i−4i−4i4i00000000000000000000000-222-22i−2i−2i2i0000000000000000
χ554-4-4-444-44−4i4i4i−4i000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ564-4-4-444-44−4i4i4i−4i00000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ5788-88-8-8-88000000000000000000000000000000000000000000000000000
χ5888-8-88-88-8000000000000000000000000000000000000000000000000000
χ598-8888-8-8-8000000000000000000000000000000000000000000000000000

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