Finite Group Databasebeta

← Group #324513

Character table — Group #324513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822224444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1
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
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1
χ91111111111111111-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ121111111111111111-1-111-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-11-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111-11-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-11-11
χ172222222222-2-2-2-22222-2-2-2-22222-2-2-2-200002-2000022-2-2000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2222200002-20000-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2222222-2-2-2-20000-220000-2-222000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-222-2-2-2-222220000-22000022-2-2000000000000000000000000
χ2122222222-2-22222-2-222-2-2220000000022-2-2-2-2-2-2220000000000000000000000000000
χ2222222222-2-22222-2-222-2-22200000000-2-222-2-222-2-20000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200000000222222-2-2-2-20000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-200000000-2-2-2-22222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000000000-2200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000000000-220000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000000002-200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000000002-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ29222-22-2-2-20022-2-2002i−2i002i−2i22−2−222−2−2002-2002i−2i00i2−i2i2−i200000000i2−i2i2−i22−22−200000000
χ30222-22-2-2-20022-2-2002i−2i002i−2i22−2−222−2−200-2200−2i2i00i2−i2i2−i200000000−i2i2−i2i2−22−2200000000
χ31222-22-2-2-20022-2-2002i−2i002i−2i−2−222−2−222002-2002i−2i00−i2i2−i2i200000000−i2i2−i2i2−22−2200000000
χ32222-22-2-2-20022-2-2002i−2i002i−2i−2−222−2−22200-2200−2i2i00−i2i2−i2i200000000i2−i2i2−i22−22−200000000
χ33222-22-2-2-20022-2-200−2i2i00−2i2i22−2−222−2−2002-200−2i2i00−i2i2−i2i200000000−i2i2−i2i22−22−200000000
χ34222-22-2-2-20022-2-200−2i2i00−2i2i22−2−222−2−200-22002i−2i00−i2i2−i2i200000000i2−i2i2−i2−22−2200000000
χ35222-22-2-2-20022-2-200−2i2i00−2i2i−2−222−2−222002-200−2i2i00i2−i2i2−i200000000i2−i2i2−i2−22−2200000000
χ36222-22-2-2-20022-2-200−2i2i00−2i2i−2−222−2−22200-22002i−2i00i2−i2i2−i200000000−i2i2−i2i22−22−200000000
χ37222-22-2-2-200-2-222002i−2i00−2i2i22−2−2−2−2222-20000002i−2ii2−i2−i2i2000000002−2−22−i2i2i2−i200000000
χ38222-22-2-2-200-2-222002i−2i00−2i2i22−2−2−2−222-22000000−2i2ii2−i2−i2i200000000−222−2i2−i2−i2i200000000
χ39222-22-2-2-200-2-222002i−2i00−2i2i−2−22222−2−22-20000002i−2i−i2i2i2−i200000000−222−2i2−i2−i2i200000000
χ40222-22-2-2-200-2-222002i−2i00−2i2i−2−22222−2−2-22000000−2i2i−i2i2i2−i2000000002−2−22−i2i2i2−i200000000
χ41222-22-2-2-200-2-22200−2i2i002i−2i22−2−2−2−2222-2000000−2i2i−i2i2i2−i2000000002−2−22i2−i2−i2i200000000
χ42222-22-2-2-200-2-22200−2i2i002i−2i22−2−2−2−222-220000002i−2i−i2i2i2−i200000000−222−2−i2i2i2−i200000000
χ43222-22-2-2-200-2-22200−2i2i002i−2i−2−22222−2−22-2000000−2i2ii2−i2−i2i200000000−222−2−i2i2i2−i200000000
χ44222-22-2-2-200-2-22200−2i2i002i−2i−2−22222−2−2-220000002i−2ii2−i2−i2i2000000002−2−22i2−i2−i2i200000000
χ4522-2-2-222-2222-22-2-2-2002-2002i−2i2i−2i2i−2i2i−2i0000000000000000002i2i−2i−2i00000000002-20000
χ4622-2-2-222-2222-22-2-2-2002-2002i−2i2i−2i2i−2i2i−2i000000000000000000−2i−2i2i2i0000000000-220000
χ4722-2-2-222-2222-22-2-2-2002-200−2i2i−2i2i−2i2i−2i2i0000000000000000002i2i−2i−2i0000000000-220000
χ4822-2-2-222-2222-22-2-2-2002-200−2i2i−2i2i−2i2i−2i2i000000000000000000−2i−2i2i2i00000000002-20000
χ4922-2-2-222-222-22-22-2-200-22002i−2i2i−2i−2i2i−2i2i000000000000002i2i−2i−2i0000000000002-2000000
χ5022-2-2-222-222-22-22-2-200-22002i−2i2i−2i−2i2i−2i2i00000000000000−2i−2i2i2i000000000000-22000000
χ5122-2-2-222-222-22-22-2-200-2200−2i2i−2i2i2i−2i2i−2i000000000000002i2i−2i−2i000000000000-22000000
χ5222-2-2-222-222-22-22-2-200-2200−2i2i−2i2i2i−2i2i−2i00000000000000−2i−2i2i2i0000000000002-2000000
χ5344-44-4-4-44004-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5444-44-4-4-44004-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5544-44-4-4-4400-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5644-44-4-4-4400-444-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5744-4-4-444-4-4-44-44-44400-44000000000000000000000000000000000000000000000000
χ5844-4-4-444-4-4-4-44-4444004-4000000000000000000000000000000000000000000000000
χ594-444-44-4-44-400004-4000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ604-444-44-4-44-400004-400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ614-444-44-4-4-440000-4400000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ624-444-44-4-4-440000-440000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ634-4-4-444-444-40000-440000000000000000000000000000000022−22−22220000000000000000
χ644-4-4-444-444-40000-4400000000000000000000000000000000−222222−220000000000000000
χ654-4-4-444-44-4400004-4000000000000000000000000000022−22−222200000000000000000000
χ664-4-4-444-44-4400004-40000000000000000000000000000−222222−2200000000000000000000
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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