Finite Group Databasebeta

← Group #254157

Character table — Group #254157

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444448888888888888816161616161616161616161616161616163232
order12222244444444444444444444444444444442244444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-111111-1-11-1-1-1-1-111-1-111-1-11-1
χ4111111111111111111111111111-1-1-1-1-1-11111-11-1-11-1-1-1-1-1-111-1-111-11
χ511111111111111111-1-1-1-111-1-1-1-111-1-11111-1-111-11111-1-11111-1-1-1-1-1-1
χ611111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ711111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-11-111-1-1-11111-1-1-1-111-11
χ811111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-111-11-1-111-1-11111-1-11-1
χ91111111111111-1-1-1-1111111-1-1-1-1111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111
χ101111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-11-1-1-1-1-1-111111111-1-1
χ111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-11111-1-111-1-1111-1
χ121111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111111-1-111-1-1-11
χ131111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-111-1-111-1-1-1-11111-1-1
χ141111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ151111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-111-111-1-1-1-11111-1-1-11
χ161111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1111-1-111-1-1-1-1111-1
χ1722222222-2-222-200002222-2-200002222-2-200-2-200-20000000000000000
χ1822222222-2-222-200002222-2-20000-2-2-2-22200-2-20020000000000000000
χ1922222222-2-222-20000-2-2-2-2-2-2000022-2-2-2-200220020000000000000000
χ2022222222-2-222-20000-2-2-2-2-2-20000-2-22222002200-20000000000000000
χ21222222-2-222-2-2222220000-2-200002-2002-2-2-200000002-2000000000000
χ22222222-2-222-2-2222220000-2-20000-2200-22-2-20000000-22000000000000
χ23222222-2-222-2-22-2-2-2-20000-2-200002-2002-2220000000-22000000000000
χ24222222-2-222-2-22-2-2-2-20000-2-20000-2200-222200000002-2000000000000
χ25222222-2-2-2-2-2-2-2000000002222-2-22-200-22000000000002-20000000000
χ26222222-2-2-2-2-2-2-2000000002222-2-2-22002-200000000000-220000000000
χ27222222-2-2-2-2-2-2-20000000022-2-2222-200-2200000000000-220000000000
χ28222222-2-2-2-2-2-2-20000000022-2-222-22002-2000000000002-20000000000
χ292222-2-22-2-2-22-222i2i−2i−2i00002-200000000002i−2i000200-20000002i−2i000000
χ302222-2-22-2-2-22-222i2i−2i−2i00002-200000000002i−2i000-2002000000−2i2i000000
χ312222-2-22-2-2-22-22−2i−2i2i2i00002-20000000000−2i2i000200-2000000−2i2i000000
χ322222-2-22-2-2-22-22−2i−2i2i2i00002-20000000000−2i2i000-20020000002i−2i000000
χ332222-2-2-22-2-2-2222i2i−2i−2i0000-220000000000−2i2i00200-2000002i−2i00000000
χ342222-2-2-22-2-2-2222i2i−2i−2i0000-220000000000−2i2i00-200200000−2i2i00000000
χ352222-2-2-22-2-2-222−2i−2i2i2i0000-2200000000002i−2i00200-200000−2i2i00000000
χ362222-2-2-22-2-2-222−2i−2i2i2i0000-2200000000002i−2i00-2002000002i−2i00000000
χ374444-4-44-4444-4-400000000-44000000000000000000000000000000000
χ384444-4-4-4444-44-4000000004-4000000000000000000000000000000000
χ394-44-400004i−4i0002+2i−2−2i2−2i−2+2i22-2-2002i−2i2-2000000002i−2i0000000000000000000
χ404-44-400004i−4i0002+2i−2−2i2−2i−2+2i-2-22200−2i2i-2200000000−2i2i0000000000000000000
χ414-44-400004i−4i000−2−2i2+2i−2+2i2−2i22-2-200−2i2i-22000000002i−2i0000000000000000000
χ424-44-400004i−4i000−2−2i2+2i−2+2i2−2i-2-222002i−2i2-200000000−2i2i0000000000000000000
χ434-44-40000−4i4i0002−2i−2+2i2+2i−2−2i22-2-200−2i2i2-200000000−2i2i0000000000000000000
χ444-44-40000−4i4i0002−2i−2+2i2+2i−2−2i-2-222002i−2i-22000000002i−2i0000000000000000000
χ454-44-40000−4i4i000−2+2i2−2i−2−2i2+2i22-2-2002i−2i-2200000000−2i2i0000000000000000000
χ464-44-40000−4i4i000−2+2i2−2i−2−2i2+2i-2-22200−2i2i2-2000000002i−2i0000000000000000000
χ474-4-444-44-400-44000000000000000000000000000000000000002i2−2i20000
χ484-4-444-44-400-4400000000000000000000000000000000000000−2i22i20000
χ494-4-444-4-44004-400000000000000000000000000000000000000002i2−2i200
χ504-4-444-4-44004-40000000000000000000000000000000000000000−2i22i200
χ514-4-44-444400-4-4000000000000000004i−4i0000000000000000000000000
χ524-4-44-444400-4-400000000000000000−4i4i0000000000000000000000000
χ534-4-44-44-4-40044000004-44-400000000000000000000000000000000000
χ544-4-44-44-4-4004400000-44-4400000000000000000000000000000000000
χ5588-8-800000000000004-4-4400000000000000000000000000000000000
χ5688-8-80000000000000-444-400000000000000000000000000000000000

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