Finite Group Databasebeta

← Group #349724

Character table — Group #349724

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1
χ91111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1111111-1-11111-1-1-1-111-1-1-1-111-11
χ101111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-11111-1-11111-1-11-1
χ111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ121111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111-1-1-1-111111111111111-1-1-1-1-1-1
χ141111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1722222222222-2-2-2-220000000022-2-2-2-2-2-22200002200002-2-20000-2-2000000000000000000
χ1822222222222-2-2-2-220000000022-2-2-2-2-2-2-2-20000-2-20000222000022000000000000000000
χ1922222222222-2-2-2-2200000000-2-22222-2-2220000-2-20000-2-2-2000022000000000000000000
χ2022222222222-2-2-2-2200000000-2-22222-2-2-2-20000220000-2220000-2-2000000000000000000
χ2122222222-2-2-22222-2222222222222-2-2-2-200000000-2-2-2-2-200000000000000000000000000
χ2222222222-2-2-22222-22222-2-2-2-2-2-2-2-222-2-200000000-2-222200000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-22222-2-2-2-222-2-20000000022-2-2200000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-22222-2-2-2-2000000002222-200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000000022-2-222220022-2-2000000-20022-2-200000000000000000000
χ2622222222-2-2-2-2-2-2-2-20000000022-2-2222200-2-222000000-200-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-222-2-2220022-2-2000000200-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-222-2-22200-2-22200000020022-2-200000000000000000000
χ29222-2-2-22-222-222-2-2-2000022-2-20000002-22-2000000002-202-22-22-200000000000000000000
χ30222-2-2-22-222-222-2-2-2000022-2-20000002-2-22000000002-20-22-22-2200000000000000000000
χ31222-2-2-22-222-222-2-2-20000-2-2220000002-22-200000000-2202-2-22-2200000000000000000000
χ32222-2-2-22-222-222-2-2-20000-2-2220000002-2-2200000000-220-222-22-200000000000000000000
χ33222-2-2-22-222-2-2-222-22i2i−2i−2i0000000000-222-22i−2i2i−2i002i−2i000-22000000000000000000000000
χ34222-2-2-22-222-2-2-222-22i2i−2i−2i0000000000-22-22−2i2i−2i2i002i−2i0002-2000000000000000000000000
χ35222-2-2-22-222-2-2-222-2−2i−2i2i2i0000000000-222-2−2i2i−2i2i00−2i2i000-22000000000000000000000000
χ36222-2-2-22-222-2-2-222-2−2i−2i2i2i0000000000-22-222i−2i2i−2i00−2i2i0002-2000000000000000000000000
χ37222-2-2-22-2-2-2222-2-22000022-2-2000000-22002i−2i−2i2i2i−2i00-2200000002i−2i000000000000000000
χ38222-2-2-22-2-2-2222-2-22000022-2-2000000-2200−2i2i2i−2i−2i2i00-220000000−2i2i000000000000000000
χ39222-2-2-22-2-2-2222-2-220000-2-222000000-22002i−2i−2i2i−2i2i002-20000000−2i2i000000000000000000
χ40222-2-2-22-2-2-2222-2-220000-2-222000000-2200−2i2i2i−2i2i−2i002-200000002i−2i000000000000000000
χ41222-2-2-22-2-2-22-2-22222i2i−2i−2i00000000002-20000002i−2i−2i2i000002-2-22−2i2i000000000000000000
χ42222-2-2-22-2-2-22-2-22222i2i−2i−2i00000000002-2000000−2i2i−2i2i00000-222-22i−2i000000000000000000
χ43222-2-2-22-2-2-22-2-2222−2i−2i2i2i00000000002-20000002i−2i2i−2i00000-222-2−2i2i000000000000000000
χ44222-2-2-22-2-2-22-2-2222−2i−2i2i2i00000000002-2000000−2i2i2i−2i000002-2-222i−2i000000000000000000
χ4522-2-2-22-220002-22-202i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000000i2i2−i2−i222−2−200002−2i2−i200
χ4622-2-2-22-220002-22-202i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000000−i2−i2i2i2−2−2220000−22−i2i200
χ4722-2-2-22-220002-22-202i−2i2i−2i-22-22−2i2i−2i2i0000000000000000000000000i2i2−i2−i2−2−22200002−2−i2i200
χ4822-2-2-22-220002-22-202i−2i2i−2i-22-22−2i2i−2i2i0000000000000000000000000−i2−i2i2i222−2−20000−22i2−i200
χ4922-2-2-22-220002-22-20−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000000i2i2−i2−i2−2−2220000−22i2−i200
χ5022-2-2-22-220002-22-20−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000000−i2−i2i2i222−2−200002−2−i2i200
χ5122-2-2-22-220002-22-20−2i2i−2i2i-22-222i−2i2i−2i0000000000000000000000000i2i2−i2−i222−2−20000−22−i2i200
χ5222-2-2-22-220002-22-20−2i2i−2i2i-22-222i−2i2i−2i0000000000000000000000000−i2−i2i2i2−2−22200002−2i2−i200
χ5344-444-4-4-40004-4-44000004-4-4400000000000000000000000000000000000000000000000
χ5444-444-4-4-40004-4-4400000-444-400000000000000000000000000000000000000000000000
χ5544-444-4-4-4000-444-404-4-44000000000000000000000000000000000000000000000000000
χ5644-444-4-4-4000-444-40-444-4000000000000000000000000000000000000000000000000000
χ5744-4-4-44-44000-44-440000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ5844-4-4-44-44000-44-44000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ594-444-4-4-444-440000-40000000000000000000000000000000000000000000000022−22000000
χ604-444-4-4-444-440000-400000000000000000000000000000000000000000000000−2222000000
χ614-444-4-4-44-44-4000040000000000000000000000000000000000000000000002i2−2i200000000
χ624-444-4-4-44-44-400004000000000000000000000000000000000000000000000−2i22i200000000
χ634-44-444-4-44-4-400004000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ644-44-444-4-44-4-40000400000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ654-44-444-4-4-4440000-4000000000000000000000000000000000000022−2222−2200000000000000
χ664-44-444-4-4-4440000-40000000000000000000000000000000000000−2222−222200000000000000
χ674-4-44-444-4000000000000000000004-4000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ684-4-44-444-4000000000000000000004-400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ694-4-44-444-400000000000000000000-44000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ704-4-44-444-400000000000000000000-4400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ718-8-8-88-888000000000000000000000000000000000000000000000000000000000000000

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