Finite Group Databasebeta

← Group #168729

Character table — Group #168729

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444442244444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ71111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-1-1-11-1-11111111-111-1-111-1-1-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-11-1-11111111-111-1-111-1-1-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-111-1-111-1-11111-1-1-1-11-1-11-1111-1-1-1-111-11
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-111-1-111-1-1-1-1-1-111111-1-11-11-1-11111-1-11-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-111-1-11-1-11111-1-1-11
χ1411111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1111111-1-1-1-1-11-111-1-1-111-1-1111-1
χ1611111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-111-1-1-1-11111-11-111-111-1-111-1-1-11
χ1722222222222222-2-2-22-2-2-2222-2000000002200000000-2-200000000000000
χ1822222222222222-2-2-22-2-2-22-2-2-200000000-2-2000000002200000000000000
χ19222222222222-2-22-2-2-2-2-22-20020000222200000000000000-2-20000000000
χ20222222222222-2-22-2-2-2-2-22-20020000-2-2-2-200000000000000220000000000
χ21222222222222-2-2-222-222-2-200-222220000000000000000-2-2000000000000
χ22222222222222-2-2-222-222-2-200-2-2-2-2-2000000000000000022000000000000
χ2322222222-2-2-2-222222-2-2-22-200-2000022-2-200000000000000-220000000000
χ2422222222-2-2-2-222222-2-2-22-200-20000-2-222000000000000002-20000000000
χ2522222222-2-2-2-222-2-2-2-222-2-200222-2-20000000000000000-22000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2002-2-22200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2222-2-2-2222200000000-2-200000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2222-2-2-22-2-220000000022000000002-200000000000000
χ29222-2-2-2-2222-2-22-2000-200022-20000000002-2i2i2−i2−i2i2i2−i2−i2000000i2−i2i2−i2000000
χ30222-2-2-2-2222-2-22-2000-200022-20000000002-2−i2−i2i2i2−i2−i2i2i2000000−i2i2−i2i2000000
χ31222-2-2-2-2222-2-22-2000-20002-22000000000-22i2i2−i2−i2i2i2−i2−i2000000−i2i2−i2i2000000
χ32222-2-2-2-2222-2-22-2000-20002-22000000000-22−i2−i2i2i2−i2−i2i2i2000000i2−i2i2−i2000000
χ33222-2-2-2-22-2-222-22000-200022-2000000000-22i2i2−i2−i2−i2−i2i2i2000000i2−i2−i2i2000000
χ34222-2-2-2-22-2-222-22000-200022-2000000000-22−i2−i2i2i2i2i2−i2−i2000000−i2i2i2−i2000000
χ35222-2-2-2-22-2-222-22000-20002-220000000002-2i2i2−i2−i2−i2−i2i2i2000000−i2i2i2−i2000000
χ36222-2-2-2-22-2-222-22000-20002-220000000002-2−i2−i2i2i2i2i2−i2−i2000000i2−i2−i2i2000000
χ372-2222-2-2-22i−2i2i−2i0002i−2i02-2000002-22i−2i0000002−22−2i2−i2i2−i200000000002−2i2−i200
χ382-2222-2-2-22i−2i2i−2i0002i−2i02-2000002-22i−2i000000−22−22−i2i2−i2i20000000000−22−i2i200
χ392-2222-2-2-22i−2i2i−2i0002i−2i02-200000-22−2i2i0000002−22−2i2−i2i2−i20000000000−22−i2i200
χ402-2222-2-2-22i−2i2i−2i0002i−2i02-200000-22−2i2i000000−22−22−i2i2−i2i200000000002−2i2−i200
χ412-2222-2-2-2−2i2i−2i2i000−2i2i02-2000002-2−2i2i0000002−22−2−i2i2−i2i200000000002−2−i2i200
χ422-2222-2-2-2−2i2i−2i2i000−2i2i02-2000002-2−2i2i000000−22−22i2−i2i2−i20000000000−22i2−i200
χ432-2222-2-2-2−2i2i−2i2i000−2i2i02-200000-222i−2i0000002−22−2−i2i2−i2i20000000000−22i2−i200
χ442-2222-2-2-2−2i2i−2i2i000−2i2i02-200000-222i−2i000000−22−22i2−i2i2−i200000000002−2−i2i200
χ45444-4-4-4-4444-4-4-440004000-40000000000000000000000000000000000000
χ46444-4-4-4-44-4-4444-40004000-40000000000000000000000000000000000000
χ4744-44-44-4-4000000400000-4000000004-40000000000000000000000000000
χ4844-44-44-4-4000000400000-400000000-440000000000000000000000000000
χ4944-44-44-4-4000000-400000400000000004i−4i00000000000000000000000000
χ5044-44-44-4-4000000-40000040000000000−4i4i00000000000000000000000000
χ514-4444-4-4-44i−4i4i−4i000−4i4i0-44000000000000000000000000000000000000000
χ524-4444-4-4-4−4i4i−4i4i0004i−4i0-44000000000000000000000000000000000000000
χ534-44-4-444-44i−4i−4i4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ544-44-4-444-44i−4i−4i4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ554-44-4-444-4−4i4i4i−4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ564-44-4-444-4−4i4i4i−4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ5788-8-88-88-8000000000000000000000000000000000000000000000000000
χ588-8-88-8-888000000000000000000000000000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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