Finite Group Databasebeta

← Group #324479

Character table — Group #324479

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822224444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ12111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11-11-1
χ172222222222-2-2-2-222-2-222220000000022-2-2-2-2-2-2220000000000000000000000000000
χ182222222222-2-2-2-222-2-2222200000000-2-222-2-222-2-20000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-200000000222222-2-2-2-20000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-200000000-2-2-2-22222220000000000000000000000000000
χ2122222222-2-22222-2-2-2-222-2-22222-2-2-2-20000-22000022-2-2000000000000000000000000
χ2222222222-2-22222-2-2-2-222-2-2-2-2-2-222220000-220000-2-222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2222222-2-2-2-200002-20000-2-222000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-222-2-2-2-2222200002-2000022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000000002-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000000002-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222000000000000-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222000000000000-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-22-2-22-200002-2002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2002-2002i−2i002−22−22−22−2i2−i2i2−i20000000000000000
χ30222-2-22-2-22-200002-2002i−2i2i−2ii2i2−i2−i2i2i2−i2−i200-2200−2i2i002−22−2−22−22−i2i2−i2i20000000000000000
χ31222-2-22-2-22-200002-2002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2002-2002i−2i00−22−22−22−22−i2i2−i2i20000000000000000
χ32222-2-22-2-22-200002-2002i−2i2i−2i−i2−i2i2i2−i2−i2i2i200-2200−2i2i00−22−222−22−2i2−i2i2−i20000000000000000
χ33222-2-22-2-22-200002-200−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2002-200−2i2i00−22−22−22−22i2−i2i2−i20000000000000000
χ34222-2-22-2-22-200002-200−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200-22002i−2i00−22−222−22−2−i2i2−i2i20000000000000000
χ35222-2-22-2-22-200002-200−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2002-200−2i2i002−22−22−22−2−i2i2−i2i20000000000000000
χ36222-2-22-2-22-200002-200−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200-22002i−2i002−22−2−22−22i2−i2i2−i20000000000000000
χ37222-2-22-2-2-220000-22002i−2i−2i2ii2i2−i2−i2−i2−i2i2i22-20000002i−2i2−2−22i2−i2−i2i2−222−20000000000000000
χ38222-2-22-2-2-220000-22002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2-22000000−2i2i2−2−22−i2i2i2−i22−2−220000000000000000
χ39222-2-22-2-2-220000-22002i−2i−2i2i−i2−i2i2i2i2i2−i2−i22-20000002i−2i−222−2−i2i2i2−i22−2−220000000000000000
χ40222-2-22-2-2-220000-22002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2-22000000−2i2i−222−2i2−i2−i2i2−222−20000000000000000
χ41222-2-22-2-2-220000-2200−2i2i2i−2ii2i2−i2−i2−i2−i2i2i22-2000000−2i2i−222−2i2−i2−i2i22−2−220000000000000000
χ42222-2-22-2-2-220000-2200−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2-220000002i−2i−222−2−i2i2i2−i2−222−20000000000000000
χ43222-2-22-2-2-220000-2200−2i2i2i−2i−i2−i2i2i2i2i2−i2−i22-2000000−2i2i2−2−22−i2i2i2−i2−222−20000000000000000
χ44222-2-22-2-2-220000-2200−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2-220000002i−2i2−2−22i2−i2−i2i22−2−220000000000000000
χ4522-22-2-2-222-222-2-2-222-200002i−2i2i−2i2i−2i2i−2i000000000000000000000022-2-200002i−2i000000
χ4622-22-2-2-222-222-2-2-222-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000-2-2220000−2i2i000000
χ4722-22-2-2-222-222-2-2-222-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000022-2-20000−2i2i000000
χ4822-22-2-2-222-222-2-2-222-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000-2-22200002i−2i000000
χ4922-22-2-2-22-2222-2-22-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000022-2-2002i−2i0000
χ5022-22-2-2-22-2222-2-22-2-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000-2-22200−2i2i0000
χ5122-22-2-2-22-2222-2-22-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000022-2-200−2i2i0000
χ5222-22-2-2-22-2222-2-22-2-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000-2-222002i−2i0000
χ5344-44-4-4-444-4-4-444-44-4400000000000000000000000000000000000000000000000000
χ5444-44-4-4-44-44-4-4444-44-400000000000000000000000000000000000000000000000000
χ5544-4-44-44-4440000-4-400000022−22−222222−22−222200000000000000000000000000000000000000
χ5644-4-44-44-4440000-4-4000000−222222−22−222222−2200000000000000000000000000000000000000
χ5744-4-44-44-4-4-400004400000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-44-44-4-4-4000044000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-44-4-4-444004-44-40000000000000000000000000000000000000022−2222−22000000000000
χ604-44-4-4-444004-44-400000000000000000000000000000000000000−2222−2222000000000000
χ614-44-4-4-44400-44-4400000000000000000000000000000000000000000022−2222−2200000000
χ624-44-4-4-44400-44-44000000000000000000000000000000000000000000−2222−222200000000
χ634-4-4-444-44004-4-440000000000000000000000000000000000000022−22−2222000000000000
χ644-4-4-444-44004-4-4400000000000000000000000000000000000000−222222−22000000000000
χ654-4-4-444-4400-444-400000000000000000000000000000000000000000022−22−222200000000
χ664-4-4-444-4400-444-4000000000000000000000000000000000000000000−222222−2200000000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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