Finite Group Databasebeta

← Group #323971

Character table — Group #323971

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244448888888844444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-11111-1-1111111111111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-1
χ91111111111111111-1-1-1-11111111111-111-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111111111111-1-1-1-11111111111-111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11-11
χ111111111111111111-1-1-1-11111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-11
χ121111111111111111-1-1-1-11111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-1-1-1111111-1-1-1-1111111-1-111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ17222222222-2-2222-2-222-2-2-2-22222-2-2-2-22000000-200-2-200002200000000000000000000
χ18222222222-2-2222-2-222-2-2-2-2-2-2-2-222222000000-200220000-2-200000000000000000000
χ19222222222-2-2222-2-2-2-222-2-22222-2-2-2-2-2000000200220000-2-200000000000000000000
χ20222222222-2-2222-2-2-2-222-2-2-2-2-2-22222-2000000200-2-200002200000000000000000000
χ2122222222-222-2-2-2222222-2-200000000-22222-2-2-2-2-20000000000000000000000000000
χ2222222222-222-2-2-2222222-2-200000000-2-2-2-2-222-2220000000000000000000000000000
χ2322222222-222-2-2-222-2-2-2-2-2-200000000222-2-2-2-22220000000000000000000000000000
χ2422222222-222-2-2-222-2-2-2-2-2-2000000002-2-222222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22200000000-2000000200002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200000000-200000020000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000002000000-200002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000000002000000-20000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ29222-22-2-2-2022000-2-22-22-20022−2−222−2−202-22-2000002−22−22−22−22−22−20000000000000000
χ30222-22-2-2-2022000-2-22-22-20022−2−222−2−20-22-22000002−2−22−222−2−22−220000000000000000
χ31222-22-2-2-2022000-2-22-22-200−2−222−2−22202-22-200000−22−22−22−22−22−220000000000000000
χ32222-22-2-2-2022000-2-22-22-200−2−222−2−2220-22-2200000−222−22−2−222−22−20000000000000000
χ33222-22-2-2-2022000-2-2-22-220022−2−222−2−202-2-2200000−222−22−2−22−22−220000000000000000
χ34222-22-2-2-2022000-2-2-22-220022−2−222−2−20-222-200000−22−22−22−222−22−20000000000000000
χ35222-22-2-2-2022000-2-2-22-2200−2−222−2−22202-2-22000002−2−22−222−22−22−20000000000000000
χ36222-22-2-2-2022000-2-2-22-2200−2−222−2−2220-222-2000002−22−22−22−2−22−220000000000000000
χ37222-22-2-2-20-2-2000222-2-220022−2−2−2−222000002i−2i02i−2i−22i2−i2−i2i22−2i2−i2−i2i20000000000000000
χ38222-22-2-2-20-2-2000222-2-220022−2−2−2−22200000−2i2i0−2i2i−22−i2i2i2−i22−2−i2i2i2−i20000000000000000
χ39222-22-2-2-20-2-2000222-2-2200−2−22222−2−2000002i−2i02i−2i2−2−i2i2i2−i2−22−i2i2i2−i20000000000000000
χ40222-22-2-2-20-2-2000222-2-2200−2−22222−2−200000−2i2i0−2i2i2−2i2−i2−i2i2−22i2−i2−i2i20000000000000000
χ41222-22-2-2-20-2-200022-222-20022−2−2−2−222000002i−2i0−2i2i2−2i2−i2−i2i2−22−i2i2i2−i20000000000000000
χ42222-22-2-2-20-2-200022-222-20022−2−2−2−22200000−2i2i02i−2i2−2−i2i2i2−i2−22i2−i2−i2i20000000000000000
χ43222-22-2-2-20-2-200022-222-200−2−22222−2−2000002i−2i0−2i2i−22−i2i2i2−i22−2i2−i2−i2i20000000000000000
χ44222-22-2-2-20-2-200022-222-200−2−22222−2−200000−2i2i02i−2i−22i2−i2−i2i22−2−i2i2i2−i20000000000000000
χ452-2-222-2-2222-22-2-22-200002-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000022-2-2002i−2i0000
χ462-2-222-2-2222-22-2-22-200002-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000-2-22200−2i2i0000
χ472-2-222-2-2222-22-2-22-200002-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000022-2-200−2i2i0000
χ482-2-222-2-2222-22-2-22-200002-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000-2-222002i−2i0000
χ492-2-222-2-222-222-2-2-220000-222i−2i2i−2i−2i2i−2i2i00000000000000000000002i2i−2i−2i00002-2000000
χ502-2-222-2-222-222-2-2-220000-222i−2i2i−2i−2i2i−2i2i0000000000000000000000−2i−2i2i2i0000-22000000
χ512-2-222-2-222-222-2-2-220000-22−2i2i−2i2i2i−2i2i−2i00000000000000000000002i2i−2i−2i0000-22000000
χ522-2-222-2-222-222-2-2-220000-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000−2i−2i2i2i00002-2000000
χ5344-44-44-4-4400-4-4400000000000000000000000000000000000000000022−2222−2200000000
χ5444-44-44-4-4400-4-44000000000000000000000000000000000000000000−2222−222200000000
χ5544-44-44-4-4-40044-40000000000000000000000000000000000000022−2222−22000000000000
χ5644-44-44-4-4-40044-400000000000000000000000000000000000000−2222−2222000000000000
χ574-444-4-44-4400-44-400000000000000000000000000000000000000000022−22−222200000000
χ584-444-4-44-4400-44-4000000000000000000000000000000000000000000−222222−2200000000
χ594-444-4-44-4-4004-44000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ604-444-4-44-4-4004-4400000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ614-4-444-4-44-44-4-4444-40000-440000000000000000000000000000000000000000000000
χ624-4-444-4-44-4-44-444-4400004-40000000000000000000000000000000000000000000000
χ634-4-4-4444-404-4000-440000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-4-4444-404-4000-44000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-4-4444-40-440004-40000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-4-4444-40-440004-4000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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