Finite Group Databasebeta

← Group #317665

Character table — Group #317665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1
χ1111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-111
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-111
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-11111-1-111-1-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1-1-11111-1-1
χ17222222222222222-2-2-2-22-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-22222-2-2-222-2-2-2-200000000000000002-22-200000000000000000000
χ20222222222222-2-2-22222-2-2-222-2-2-2-20000000000000000-22-2200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-2222-2-2-2-22-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2-2222200000000000000002-2-2200000000000000000000
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-222220000000000000000-222-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000000000000000000000−2i2i2i−2i
χ29222-2-2-22-200002-2-222-2-222-20000002i2i−2i−2i2i2i−2i−2i000000000000002i−2i002-2000000000000
χ30222-2-2-22-200002-2-222-2-222-20000002i2i−2i−2i2i2i−2i−2i00000000000000−2i2i00-22000000000000
χ31222-2-2-22-200002-2-222-2-222-2000000−2i−2i2i2i−2i−2i2i2i000000000000002i−2i00-22000000000000
χ32222-2-2-22-200002-2-222-2-222-2000000−2i−2i2i2i−2i−2i2i2i00000000000000−2i2i002-2000000000000
χ33222-2-2-22-200002-2-2-2-2222-220000002i2i−2i−2i−2i−2i2i2i0000000000002-2002i−2i00000000000000
χ34222-2-2-22-200002-2-2-2-2222-220000002i2i−2i−2i−2i−2i2i2i000000000000-2200−2i2i00000000000000
χ35222-2-2-22-200002-2-2-2-2222-22000000−2i−2i2i2i2i2i−2i−2i0000000000002-200−2i2i00000000000000
χ36222-2-2-22-200002-2-2-2-2222-22000000−2i−2i2i2i2i2i−2i−2i000000000000-22002i−2i00000000000000
χ372-2-22-2-22222-2-222-20000-20000002-22-22-2000022-2-20000000000000000i2−i2i2−i2i2−i2i2−i20000
χ382-2-22-2-22222-2-222-20000-20000002-22-22-2000022-2-20000000000000000−i2i2−i2i2−i2i2−i2i20000
χ392-2-22-2-22222-2-222-20000-20000002-2-22-220000-2-2220000000000000000i2−i2i2−i2−i2i2−i2i20000
χ402-2-22-2-22222-2-222-20000-20000002-2-22-220000-2-2220000000000000000−i2i2−i2i2i2−i2i2−i20000
χ412-2-22-2-222-2-22222-20000-2000000-222-22-20000-2-2220000000000000000i2−i2−i2i2i2−i2−i2i20000
χ422-2-22-2-222-2-22222-20000-2000000-222-22-20000-2-2220000000000000000−i2i2i2−i2−i2i2i2−i20000
χ432-2-22-2-222-2-22222-20000-2000000-22-22-22000022-2-20000000000000000i2−i2−i2i2−i2i2i2−i20000
χ442-2-22-2-222-2-22222-20000-2000000-22-22-22000022-2-20000000000000000−i2i2i2−i2i2−i2−i2i20000
χ45444-4-4-44-40000-44444-4-4-4-440000000000000000000000000000000000000000000000
χ46444-4-4-44-40000-444-4-444-44-40000000000000000000000000000000000000000000000
χ4744-444-4-4-400000000000000004-400000022−2222−2222−2222−220000000000000000000000000000
χ4844-444-4-4-400000000000000004-4000000−2222−2222−2222−22220000000000000000000000000000
χ4944-444-4-4-40000000000000000-4400000022−2222−22−2222−22220000000000000000000000000000
χ5044-444-4-4-40000000000000000-44000000−2222−222222−2222−220000000000000000000000000000
χ5144-4-4-44-444i−4i4i−4i000000000000000000002i2−2i2−2i22i200002222−22−22000000000000000000000000
χ5244-4-4-44-444i−4i4i−4i00000000000000000000−2i22i22i2−2i20000−22−222222000000000000000000000000
χ5344-4-4-44-44−4i4i−4i4i000000000000000000002i2−2i2−2i22i20000−22−222222000000000000000000000000
χ5444-4-4-44-44−4i4i−4i4i00000000000000000000−2i22i22i2−2i200002222−22−22000000000000000000000000
χ554-444-44-4-400000004-44-40000000000000000022−22−222222−2222−22000000000000000000000000
χ564-444-44-4-400000004-44-400000000000000000−222222−22−2222−2222000000000000000000000000
χ574-444-44-4-40000000-44-440000000000000000022−22−2222−2222−2222000000000000000000000000
χ584-444-44-4-40000000-44-4400000000000000000−222222−2222−2222−22000000000000000000000000
χ594-44-44-4-444i−4i−4i4i0004-4-440004i−4i00000000000000000000000000000000000000000000
χ604-44-44-4-444i−4i−4i4i000-444-4000−4i4i00000000000000000000000000000000000000000000
χ614-44-44-4-44−4i4i4i−4i0004-4-44000−4i4i00000000000000000000000000000000000000000000
χ624-44-44-4-44−4i4i4i−4i000-444-40004i−4i00000000000000000000000000000000000000000000
χ634-4-44-4-44444-4-4-4-4400004000000-440000000000000000000000000000000000000000
χ644-4-44-4-444-4-444-4-44000040000004-40000000000000000000000000000000000000000
χ654-4-4-4444-400004-440000-4000000004i−4i−4i4i000000000000000000000000000000000000
χ664-4-4-4444-400004-440000-400000000−4i4i4i−4i000000000000000000000000000000000000
χ674-4-4-4444-40000-44-400004000000000000000000004-4-44000000000000000000000000
χ684-4-4-4444-40000-44-40000400000000000000000000-444-4000000000000000000000000

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