Finite Group Databasebeta

← Group #254708

Character table — Group #254708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222222224444444444444444442244444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-111-1-111111111-11-1111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-1-11111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-1111111-1-1111111-1-1-1-1-11-11-1-11-1-1111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111-111-111-1-1-1-111-1-111
χ11111111111111-1-1-1-1111111-1-111-1-1-1-11111-11-11-1-11-1-11-1-111-1-111-1-111
χ12111111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-111-1-1-11111-1-111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-11-1111-1-11-1-111-1-11111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-11-1111-1-1111-1-111-1-1-1-111
χ172222222222222222-2-2-2-222-2-2-2-200000000-2020000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2220000000020-20000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-20000000020-20000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2222200000000-2020000000000000000000
χ2122222222-2-2-2-222-2-222-2-2002-2000000000000000022-2-2000000000000
χ2222222222-2-2-2-222-2-222-2-2002-20000000000000000-2-222000000000000
χ2322222222-2-2-2-222-2-2-2-22200-220000000000020-22-20000000000000000
χ2422222222-2-2-2-222-2-2-2-22200-2200000000000-202-220000000000000000
χ2522222222-2-2-2-2-2-22222-2-200-2200000000000000002-22-2000000000000
χ2622222222-2-2-2-2-2-22222-2-200-220000000000000000-22-22000000000000
χ2722222222-2-2-2-2-2-222-2-222002-20000000000020-2-220000000000000000
χ2822222222-2-2-2-2-2-222-2-222002-200000000000-2022-20000000000000000
χ292-222-2-22-222-2-200002-22-22-2002-200002i2i−2i−2i0000000000002i−2i00000000
χ302-222-2-22-222-2-200002-22-22-2002-20000−2i−2i2i2i000000000000−2i2i00000000
χ312-222-2-22-222-2-200002-22-2-2200-2200002i2i−2i−2i000000000000−2i2i00000000
χ322-222-2-22-222-2-200002-22-2-2200-220000−2i−2i2i2i0000000000002i−2i00000000
χ332-222-2-22-222-2-20000-22-222-200-222i2i−2i−2i000000000000002i−2i0000000000
χ342-222-2-22-222-2-20000-22-222-200-22−2i−2i2i2i00000000000000−2i2i0000000000
χ352-222-2-22-222-2-20000-22-22-22002-22i2i−2i−2i00000000000000−2i2i0000000000
χ362-222-2-22-222-2-20000-22-22-22002-2−2i−2i2i2i000000000000002i−2i0000000000
χ37444-4-4-4-444-44-40000000000000000000000000000000000000000002i2−2i2
χ38444-4-4-4-444-44-4000000000000000000000000000000000000000000−2i22i2
χ39444-4-4-4-44-44-4400000000000000000000000000000000000000002i2−2i200
χ40444-4-4-4-44-44-440000000000000000000000000000000000000000−2i22i200
χ4144-4-44-44-40000004-400000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ4244-4-44-44-40000004-40000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ4344-4-44-44-4000000-4400000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ4444-4-44-44-4000000-440000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ454-444-4-44-4-4-44400004-4-44000000000000000000000000000000000000
χ464-444-4-44-4-4-4440000-444-4000000000000000000000000000000000000
χ474-44-444-4-44-4-44000000000000000000000000000000000000002i2−2i20000
χ484-44-444-4-44-4-4400000000000000000000000000000000000000−2i22i20000
χ494-44-444-4-4-444-40000000000000000000000000000000000002i2−2i2000000
χ504-44-444-4-4-444-4000000000000000000000000000000000000−2i22i2000000
χ514-4-4-4-444400004-40000000000002-2-222-2-220000000000000000000000
χ524-4-4-4-444400004-4000000000000-222-2-222-20000000000000000000000
χ534-4-4-4-44440000-440000000000002-2-22-222-20000000000000000000000
χ544-4-4-4-44440000-44000000000000-222-22-2-220000000000000000000000
χ5588-88-88-8-8000000000000000000000000000000000000000000000000
χ568-8-888-8-88000000000000000000000000000000000000000000000000

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