Finite Group Databasebeta

← Group #168893

Character table — Group #168893

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
χ311111111111111111111111111-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-11111-1-11-1-111111111-1-11-1-111111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-111-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-111
χ911111111-1-1-1-11-1-1-1-11111111-1-111-1-111-1-1-11111-1-1-1-11-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-1-1-11111111-1-111-1-111-1-1-1-1-1-1-111111-111-1-1-1-111-1-111-11
χ1111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1111111-1-1-1-11-1-1-111-1-111-1-1111-1
χ1211111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-111-1-1-1-111111-1-1-11111-1-111-1-1-11
χ1311111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1111111-1-1-1-1-111-11-111-1-1-1-111-11
χ1411111111-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-111-1-1-1-11111-111-11-1-1-11111-1-11-1
χ1511111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-11111-1-1-1-1-11-11-11-1-11111-1-1-11
χ1611111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-11111-11-11-1111-1-1-1-1111-1
χ172222222222222-2-2-2-2-2-2-2-22222200000020000000000-2-200000000000000
χ182222222222222-2-2-2-2-2-2-2-22-2-2-2-2000000200000000002200000000000000
χ19222222222222-222-2-222-2-2-20000000022-22200000000000-2-200000000000
χ20222222222222-222-2-222-2-2-200000000-2-2-2-2-2000000000002200000000000
χ21222222222222-2-2-222-2-222-20000222200-2000000000000-200-20000000000
χ22222222222222-2-2-222-2-222-20000-2-2-2-200-200000000000020020000000000
χ2322222222-2-2-2-222222-2-2-2-2222-2-2000000-20000000000-2200000000000000
χ2422222222-2-2-2-222222-2-2-2-22-2-222000000-200000000002-200000000000000
χ2522222222-2-2-2-2-222-2-2-2-222-2000022-2-2002000000000000-20020000000000
χ2622222222-2-2-2-2-222-2-2-2-222-20000-2-222002000000000000200-20000000000
χ2722222222-2-2-2-2-2-2-22222-2-2-200000000222-2-200000000000-2200000000000
χ2822222222-2-2-2-2-2-2-22222-2-2-200000000-2-2222000000000002-200000000000
χ29222-2-2-2-222i2i−2i−2i0002i−2i002-2000002-22i−2i0000022−2−2i2i2−i2−i20000002−2i2−i2000000
χ30222-2-2-2-222i2i−2i−2i0002i−2i002-2000002-22i−2i00000−2−222−i2−i2i2i2000000−22−i2i2000000
χ31222-2-2-2-222i2i−2i−2i0002i−2i002-200000-22−2i2i0000022−2−2i2i2−i2−i2000000−22−i2i2000000
χ32222-2-2-2-222i2i−2i−2i0002i−2i002-200000-22−2i2i00000−2−222−i2−i2i2i20000002−2i2−i2000000
χ33222-2-2-2-22−2i−2i2i2i000−2i2i002-2000002-2−2i2i0000022−2−2−i2−i2i2i20000002−2−i2i2000000
χ34222-2-2-2-22−2i−2i2i2i000−2i2i002-2000002-2−2i2i00000−2−222i2i2−i2−i2000000−22i2−i2000000
χ35222-2-2-2-22−2i−2i2i2i000−2i2i002-200000-222i−2i0000022−2−2−i2−i2i2i2000000−22i2−i2000000
χ36222-2-2-2-22−2i−2i2i2i000−2i2i002-200000-222i−2i00000−2−222i2i2−i2−i20000002−2−i2i2000000
χ372-2-222-2-222i−2i2i−2i02i−2i002-2000000000002i−2i02-2i2−i2i2−i22−22−200000000002−2i2−i200
χ382-2-222-2-222i−2i2i−2i02i−2i002-2000000000002i−2i02-2−i2i2−i2i2−22−220000000000−22−i2i200
χ392-2-222-2-222i−2i2i−2i02i−2i002-200000000000−2i2i0-22i2−i2i2−i22−22−20000000000−22−i2i200
χ402-2-222-2-222i−2i2i−2i02i−2i002-200000000000−2i2i0-22−i2i2−i2i2−22−2200000000002−2i2−i200
χ412-2-222-2-22−2i2i−2i2i0−2i2i002-2000000000002i−2i0-22i2−i2i2−i2−22−2200000000002−2−i2i200
χ422-2-222-2-22−2i2i−2i2i0−2i2i002-2000000000002i−2i0-22−i2i2−i2i22−22−20000000000−22i2−i200
χ432-2-222-2-22−2i2i−2i2i0−2i2i002-200000000000−2i2i02-2i2−i2i2−i2−22−220000000000−22i2−i200
χ442-2-222-2-22−2i2i−2i2i0−2i2i002-200000000000−2i2i02-2−i2i2−i2i22−22−200000000002−2−i2i200
χ45444-4-4-4-444i4i−4i−4i000−4i4i00-4400000000000000000000000000000000000000
χ46444-4-4-4-44−4i−4i4i4i0004i−4i00-4400000000000000000000000000000000000000
χ4744-44-44-4-40000400000000-44-400000000000000000000000000000000000
χ4844-44-44-4-40000400000000-4-4400000000000000000000000000000000000
χ4944-44-44-4-40000-4000000004004i−4i000000000000000000000000000000000
χ5044-44-44-4-40000-400000000400−4i4i000000000000000000000000000000000
χ514-4-444-4-444i−4i4i−4i0−4i4i00-440000000000000000000000000000000000000000
χ524-4-444-4-44−4i4i−4i4i04i−4i00-440000000000000000000000000000000000000000
χ534-4-4-4-44444-4-44000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ544-4-4-4-44444-4-4400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ554-4-4-4-4444-444-4000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ564-4-4-4-4444-444-400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5788-8-88-88-8000000000000000000000000000000000000000000000000000
χ588-888-8-88-8000000000000000000000000000000000000000000000000000
χ598-88-888-8-8000000000000000000000000000000000000000000000000000

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