Finite Group Databasebeta

← Group #256413

Character table — Group #256413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222244444444224444444444442244444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-11-1-11-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-11-111-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-11111-1-1-11-1-11-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-11-1-11-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-111111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1111111-1-1-1-1111-1-11-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1111111-1-1-1-111-111-11-1-1-1-1111-1-1-1-111-1-111
χ11111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1111-1-11-1-1-11111-1-1-1-111
χ12111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-111-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-111111111-111-11-1-1-1-11-1-11111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1111-1-11-111-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111111-1-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-20000220000-2-200000200-20000000000000
χ182222222222222222-2-2-2-2-2-20000-2-200002200000-20020000000000000
χ19222222222222-2-2-2-2-2-2-2-2220000220000-2-200000-20020000000000000
χ20222222222222-2-2-2-2-2-2-2-2220000-2-200002200000200-20000000000000
χ2122222222-2-2-2-222-2-222-2-22-20000000000000200-202-200000000000000
χ2222222222-2-2-2-222-2-222-2-22-20000000000000-20020-2200000000000000
χ2322222222-2-2-2-222-2-2-2-222-22000000000000202-200000-2000000000000
χ2422222222-2-2-2-222-2-2-2-222-22000000000000-20-22000002000000000000
χ2522222222-2-2-2-2-2-22222-2-2-220000000000000200-20-2200000000000000
χ2622222222-2-2-2-2-2-22222-2-2-220000000000000-200202-200000000000000
χ2722222222-2-2-2-2-2-222-2-2222-200000000000020-2-2000002000000000000
χ2822222222-2-2-2-2-2-222-2-2222-2000000000000-202200000-2000000000000
χ2922-222-2-2-22-2-2200002-22-20000002i−2i2i2i−2i−2i2i−2i0000000000002-200000000
χ3022-222-2-2-22-2-2200002-22-20000002i−2i−2i−2i2i2i2i−2i000000000000-2200000000
χ3122-222-2-2-22-2-2200002-22-2000000−2i2i2i2i−2i−2i−2i2i000000000000-2200000000
χ3222-222-2-2-22-2-2200002-22-2000000−2i2i−2i−2i2i2i−2i2i0000000000002-200000000
χ3322-222-2-2-22-2-220000-22-22002i2i−2i−2i2i−2i0000−2i2i00000000002-20000000000
χ3422-222-2-2-22-2-220000-22-22002i2i−2i−2i−2i2i00002i−2i0000000000-220000000000
χ3522-222-2-2-22-2-220000-22-2200−2i−2i2i2i2i−2i0000−2i2i0000000000-220000000000
χ3622-222-2-2-22-2-220000-22-2200−2i−2i2i2i−2i2i00002i−2i00000000002-20000000000
χ3744-444-4-4-4-444-400004-4-44000000000000000000000000000000000000
χ3844-444-4-4-4-444-40000-444-4000000000000000000000000000000000000
χ394-444-44-4-400004-4000000002i−2i2i−2i002i−2i2i−2i000000000000000000000000
χ404-444-44-4-400004-400000000−2i2i−2i2i00−2i2i−2i2i000000000000000000000000
χ414-444-44-4-40000-44000000002i−2i2i−2i00−2i2i−2i2i000000000000000000000000
χ424-444-44-4-40000-4400000000−2i2i−2i2i002i−2i2i−2i000000000000000000000000
χ434-44-44-4-4444-4-40000000000000000000000000000000000000000002i2−2i2
χ444-44-44-4-4444-4-4000000000000000000000000000000000000000000−2i22i2
χ454-44-44-4-44-4-444000000000000000000000000000000000000000022−2200
χ464-44-44-4-44-4-4440000000000000000000000000000000000000000−222200
χ474-4-44-4-4440000004-40000002-2-22002-2-22000000000000000000000000
χ484-4-44-4-4440000004-4000000-222-200-222-2000000000000000000000000
χ494-4-44-4-444000000-440000002-2-2200-222-2000000000000000000000000
χ504-4-44-4-444000000-44000000-222-2002-2-22000000000000000000000000
χ514-4-4-4444-44-44-4000000000000000000000000000000000000002i2−2i20000
χ524-4-4-4444-44-44-400000000000000000000000000000000000000−2i22i20000
χ534-4-4-4444-4-44-4400000000000000000000000000000000000022−22000000
χ544-4-4-4444-4-44-44000000000000000000000000000000000000−2222000000
χ55888-8-8-88-8000000000000000000000000000000000000000000000000
χ5688-8-8-88-88000000000000000000000000000000000000000000000000

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