Finite Group Databasebeta

← Group #254150

Character table — Group #254150

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444448888888888888816161616161616161616161616161616163232
order12222244444444444444444224444444444442244444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111-1-11111-11-1-11-1-1-1-111-1-111-1-11-1
χ41111111111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-111-1-111-11
χ511111111111111111-1-1-1-111-1-11111-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111
χ611111111111111111-1-1-1-111-1-11111-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-1-111111-1-111-1-1111-1
χ811111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1111111-1-111-1-1-11
χ91111111111111-1-1-1-1111111-1-111-1-1-1-111-1-111-11111-1-1111111-1-1-1-1-1-1
χ101111111111111-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-111-1-1-1-1111111
χ111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1111-1-111-1-1-1-111-11
χ121111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111-111-111-1-1-1-11111-1-11-1
χ131111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ141111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ151111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11-1-111-1-11111-1-1-11
χ161111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11-111-1-1-11111-1-1-1-1111-1
χ1722222222-2-222-222220000-2-20022-2-200-2-2-2-2002000000000000000000
χ1822222222-2-222-222220000-2-200-2-2220022-2-200-2000000000000000000
χ1922222222-2-222-2-2-2-2-20000-2-200222200-2-22200-2000000000000000000
χ2022222222-2-222-2-2-2-2-20000-2-200-2-2-2-2002222002000000000000000000
χ21222222-2-222-2-2200002222-2-2002-200002-200-2-200000002-20000000000
χ22222222-2-222-2-2200002222-2-200-220000-2200-2-20000000-220000000000
χ23222222-2-222-2-220000-2-2-2-2-2-2002-200002-200220000000-220000000000
χ24222222-2-222-2-220000-2-2-2-2-2-200-220000-22002200000002-20000000000
χ25222222-2-2-2-2-2-2-20000000022222-200-2-2-220000000002-2000000000000
χ26222222-2-2-2-2-2-2-2000000002222-2200-2-22-2000000000-22000000000000
χ27222222-2-2-2-2-2-2-20000000022-2-22-20022-22000000000-22000000000000
χ28222222-2-2-2-2-2-2-20000000022-2-2-2200222-20000000002-2000000000000
χ292222-2-22-2-2-22-2200002i2i−2i−2i2-20000000000002i−2i002-200000002i−2i000000
χ302222-2-22-2-2-22-2200002i2i−2i−2i2-20000000000002i−2i00-220000000−2i2i000000
χ312222-2-22-2-2-22-220000−2i−2i2i2i2-2000000000000−2i2i002-20000000−2i2i000000
χ322222-2-22-2-2-22-220000−2i−2i2i2i2-2000000000000−2i2i00-2200000002i−2i000000
χ332222-2-2-22-2-2-22200002i2i−2i−2i-22000000000000−2i2i0200-200002i−2i00000000
χ342222-2-2-22-2-2-22200002i2i−2i−2i-22000000000000−2i2i0-20020000−2i2i00000000
χ352222-2-2-22-2-2-2220000−2i−2i2i2i-220000000000002i−2i0200-20000−2i2i00000000
χ362222-2-2-22-2-2-2220000−2i−2i2i2i-220000000000002i−2i0-200200002i−2i00000000
χ374444-4-44-4444-4-400000000-44000000000000000000000000000000000
χ384444-4-4-4444-44-4000000004-4000000000000000000000000000000000
χ3944-4-400004i−4i00022-2-22+2i−2−2i2−2i−2+2i002-200002i−2i002i−2i000000000000000000000
χ4044-4-400004i−4i00022-2-2−2−2i2+2i−2+2i2−2i00-220000−2i2i002i−2i000000000000000000000
χ4144-4-400004i−4i000-2-2222+2i−2−2i2−2i−2+2i00-220000−2i2i00−2i2i000000000000000000000
χ4244-4-400004i−4i000-2-222−2−2i2+2i−2+2i2−2i002-200002i−2i00−2i2i000000000000000000000
χ4344-4-40000−4i4i00022-2-22−2i−2+2i2+2i−2−2i002-20000−2i2i00−2i2i000000000000000000000
χ4444-4-40000−4i4i00022-2-2−2+2i2−2i−2−2i2+2i00-2200002i−2i00−2i2i000000000000000000000
χ4544-4-40000−4i4i000-2-2222−2i−2+2i2+2i−2−2i00-2200002i−2i002i−2i000000000000000000000
χ4644-4-40000−4i4i000-2-222−2+2i2−2i−2−2i2+2i002-20000−2i2i002i−2i000000000000000000000
χ474-4-444-44-400-4404i−4i4i−4i000000000000000000000000000000000000000
χ484-4-444-44-400-440−4i4i−4i4i000000000000000000000000000000000000000
χ494-4-444-4-44004-40000000000000004i−4i000000000000000000000000000
χ504-4-444-4-44004-4000000000000000−4i4i000000000000000000000000000
χ514-4-44-444400-4-400000000000000000000000000000000000000002i2−2i200
χ524-4-44-444400-4-40000000000000000000000000000000000000000−2i22i200
χ534-4-44-44-4-400440000000000000000000000000000000000000022−220000
χ544-4-44-44-4-4004400000000000000000000000000000000000000−22220000
χ558-88-80000000004i−4i−4i4i000000000000000000000000000000000000000
χ568-88-8000000000−4i4i4i−4i000000000000000000000000000000000000000

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