Finite Group Databasebeta

← Group #254156

Character table — Group #254156

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444448888888888888816161616161616161616161616161616163232
order12222244444444444444444444444444444442444444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-1-1-111111-1-11-1-1-1-1-111-1-111-1-11-1
χ41111111111111111111111111-1-111-1-1-1-11111-11-1-11-1-1-1-1-1-111-1-111-11
χ511111111111111111-1-1-1-111-1-111-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111
χ611111111111111111-1-1-1-111-1-111-1-1111111-1-1-1-11-1-1-1-1-1-111111111-1-1
χ711111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11111-1-111-1-1111-1
χ811111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-1-11111111-1-111-1-1-11
χ91111111111111-1-1-1-1111111-1-111-1-111-1-1-1-11111-111-1-1111111-1-1-1-1-1-1
χ101111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1111111
χ111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-111-111-1-111-1-1-1-111-11
χ121111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-111-1111-1-1-1-11111-1-11-1
χ131111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11111-1-1-1-1-1-11111-1-1
χ141111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ151111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11-111-1-1-111-1-11111-1-1-11
χ161111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-111-11-1-11111-1-1-1-1111-1
χ1722222222-2-222-222220000-2-2002200-2-222-2-20000-20000000000000000
χ1822222222-2-222-222220000-2-200-2-20022-2-2-2-2000020000000000000000
χ1922222222-2-222-2-2-2-2-20000-2-2002200-2-2-2-222000020000000000000000
χ2022222222-2-222-2-2-2-2-20000-2-200-2-2002222220000-20000000000000000
χ21222222-2-222-2-2200002222-2-2002-2002-20000-2-200000002-20000000000
χ22222222-2-222-2-2200002222-2-200-2200-220000-2-20000000-220000000000
χ23222222-2-222-2-220000-2-2-2-2-2-2002-2002-20000220000000-220000000000
χ24222222-2-222-2-220000-2-2-2-2-2-200-2200-2200002200000002-20000000000
χ25222222-2-2-2-2-2-2-20000000022222-2-2-2-22000000000002-2000000000000
χ26222222-2-2-2-2-2-2-2000000002222-22-2-22-200000000000-22000000000000
χ27222222-2-2-2-2-2-2-20000000022-2-22-222-2200000000000-22000000000000
χ28222222-2-2-2-2-2-2-20000000022-2-2-22222-2000000000002-2000000000000
χ292222-2-22-2-2-22-2200002i2i−2i−2i2-20000000000002i−2i0200-20000002i−2i000000
χ302222-2-22-2-2-22-2200002i2i−2i−2i2-20000000000002i−2i0-2002000000−2i2i000000
χ312222-2-22-2-2-22-220000−2i−2i2i2i2-2000000000000−2i2i0200-2000000−2i2i000000
χ322222-2-22-2-2-22-220000−2i−2i2i2i2-2000000000000−2i2i0-20020000002i−2i000000
χ332222-2-2-22-2-2-22200002i2i−2i−2i-22000000000000−2i2i200-2000002i−2i00000000
χ342222-2-2-22-2-2-22200002i2i−2i−2i-22000000000000−2i2i-200200000−2i2i00000000
χ352222-2-2-22-2-2-2220000−2i−2i2i2i-220000000000002i−2i200-200000−2i2i00000000
χ362222-2-2-22-2-2-2220000−2i−2i2i2i-220000000000002i−2i-2002000002i−2i00000000
χ374444-4-44-4444-4-400000000-44000000000000000000000000000000000
χ384444-4-4-4444-44-4000000004-4000000000000000000000000000000000
χ394-44-44-44400-4-4000000000000000000000000000000000000000022−2200
χ404-44-44-44400-4-40000000000000000000000000000000000000000−222200
χ414-44-44-4-4-40044000000000000000000000000000000000000002i2−2i20000
χ424-44-44-4-4-4004400000000000000000000000000000000000000−2i22i20000
χ434-44-4-444-400-4404i4i−4i−4i000000000000000000000000000000000000000
χ444-44-4-444-400-440−4i−4i4i4i000000000000000000000000000000000000000
χ454-44-4-44-44004-400000000000000000004i−4i00000000000000000000000
χ464-44-4-44-44004-40000000000000000000−4i4i00000000000000000000000
χ474-4-4400004i−4i0002i−2i2i−2i2+2i−2−2i2−2i−2+2i002i−2i002-200002-2000000000000000000000
χ484-4-4400004i−4i0002i−2i2i−2i−2−2i2+2i−2+2i2−2i00−2i2i00-2200002-2000000000000000000000
χ494-4-4400004i−4i000−2i2i−2i2i2+2i−2−2i2−2i−2+2i00−2i2i00-220000-22000000000000000000000
χ504-4-4400004i−4i000−2i2i−2i2i−2−2i2+2i−2+2i2−2i002i−2i002-20000-22000000000000000000000
χ514-4-440000−4i4i0002i−2i2i−2i2−2i−2+2i2+2i−2−2i002i−2i00-220000-22000000000000000000000
χ524-4-440000−4i4i0002i−2i2i−2i−2+2i2−2i−2−2i2+2i00−2i2i002-20000-22000000000000000000000
χ534-4-440000−4i4i000−2i2i−2i2i2−2i−2+2i2+2i−2−2i00−2i2i002-200002-2000000000000000000000
χ544-4-440000−4i4i000−2i2i−2i2i−2+2i2−2i−2−2i2+2i002i−2i00-2200002-2000000000000000000000
χ5588-8-80000000004-4-44000000000000000000000000000000000000000
χ5688-8-8000000000-444-4000000000000000000000000000000000000000

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