Finite Group Databasebeta

← Group #290791

Character table — Group #290791

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-11-1111-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-11-1111-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-11-1-1-11111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-111-1-1-1-11-11-1-111-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-111-1-1-1-11-11-1-111-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-111-1-1-1-1-11-111-1-1111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111111111-1-111-1-1-1-1-11-111-1-11-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11111-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11111-1-1-11111-1-111-1-1-1-111
χ172222222222222222-2-22222-2-2-2-2-2-222-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-222-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000
χ2122222222-2-2-2-222-2-22-200002-22-2000000020002-2-20000000000000000
χ2222222222-2-2-2-222-2-22-200002-22-20000000-2000-2220000000000000000
χ2322222222-2-2-2-222-2-2-220000-22-2200000020-22-20000000000000000000
χ2422222222-2-2-2-222-2-2-220000-22-22000000-202-220000000000000000000
χ2522222222-2-2-2-2-2-2222-200002-2-2200000002000-22-20000000000000000
χ2622222222-2-2-2-2-2-2222-200002-2-220000000-20002-220000000000000000
χ2722222222-2-2-2-2-2-222-220000-222-200000020-2-220000000000000000000
χ2822222222-2-2-2-2-2-222-220000-222-2000000-2022-20000000000000000000
χ2922-2-222-2-22-22-200002-22i2i−2i−2i-22002i−2i00000000000000000000002-2002i−2i
χ3022-2-222-2-22-22-200002-22i2i−2i−2i-22002i−2i0000000000000000000000-2200−2i2i
χ3122-2-222-2-22-22-200002-2−2i−2i2i2i-2200−2i2i00000000000000000000002-200−2i2i
χ3222-2-222-2-22-22-200002-2−2i−2i2i2i-2200−2i2i0000000000000000000000-22002i−2i
χ3322-2-222-2-22-22-20000-222i2i−2i−2i2-200−2i2i000000000000000000002i−2i002-200
χ3422-2-222-2-22-22-20000-222i2i−2i−2i2-200−2i2i00000000000000000000−2i2i00-2200
χ3522-2-222-2-22-22-20000-22−2i−2i2i2i2-2002i−2i000000000000000000002i−2i00-2200
χ3622-2-222-2-22-22-20000-22−2i−2i2i2i2-2002i−2i00000000000000000000−2i2i002-200
χ37444-4-4-44-44-4-4400000000000000004-400000000000000000000000000
χ38444-4-4-44-44-4-440000000000000000-4400000000000000000000000000
χ39444-4-4-44-4-444-40000004-44-40000000000000000000000000000000000
χ40444-4-4-44-4-444-4000000-44-440000000000000000000000000000000000
χ4144-44-4-4-4444-4-40000000000000000004-4000000000000000000000000
χ4244-44-4-4-4444-4-4000000000000000000-44000000000000000000000000
χ4344-44-4-4-44-4-4440000004i−4i−4i4i0000000000000000000000000000000000
χ4444-44-4-4-44-4-444000000−4i4i4i−4i0000000000000000000000000000000000
χ4544-4-444-4-4-44-440000440000-4-400000000000000000000000000000000
χ4644-4-444-4-4-44-440000-4-400004400000000000000000000000000000000
χ474-44-44-4-440000004-40000000000000000000000002i−2i2i−2i000000000000
χ484-44-44-4-440000004-4000000000000000000000000−2i2i−2i2i000000000000
χ494-44-44-4-44000000-440000000000000000000000002i−2i−2i2i000000000000
χ504-44-44-4-44000000-44000000000000000000000000−2i2i2i−2i000000000000
χ514-4-4-4-444400004-40000000000000000000000000000002-22-200000000
χ524-4-4-4-444400004-4000000000000000000000000000000-22-2200000000
χ534-4-4-4-44440000-440000000000000000000000000000002-2-2200000000
χ544-4-4-4-44440000-44000000000000000000000000000000-222-200000000
χ558-888-88-8-8000000000000000000000000000000000000000000000000
χ568-8-888-88-8000000000000000000000000000000000000000000000000

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