Finite Group Databasebeta

← Group #331027

Character table — Group #331027

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order12222244444444444488884488888824448888888888884444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1111-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-111-1-1-1-1111111-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11-1-11111-1-111-1-11-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11-1-111-1-111-1-111-11-11
χ111111111111-1-1-1-111111111-1-1-1-1-1-111-111-111-1-111-1-111-1-1-11-11
χ121111111111-1-1-1-111111111-1-1-1-1-1-111-111-111-1-1-1-111-1-1111-11-1
χ131111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1111-1-11
χ141111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-111-1
χ151111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-111-1
χ161111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-11-1-11
χ1722222222222222-2-2-2-22222-2-222-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000
χ192222222222-2-2-2-2-2-2-2-2222222-2-222-2-200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000
χ212222-2-222-2-2000022-2-22i2i−2i−2i0000002i−2i02-202i−2i00000000000000
χ222222-2-222-2-2000022-2-22i2i−2i−2i0000002i−2i0-220−2i2i00000000000000
χ232222-2-222-2-2000022-2-2−2i−2i2i2i000000−2i2i02-20−2i2i00000000000000
χ242222-2-222-2-2000022-2-2−2i−2i2i2i000000−2i2i0-2202i−2i00000000000000
χ252222-2-222-2-20000-2-2222i2i−2i−2i000000−2i2i200-2002i−2i000000000000
χ262222-2-222-2-20000-2-2222i2i−2i−2i000000−2i2i-200200−2i2i000000000000
χ272222-2-222-2-20000-2-222−2i−2i2i2i0000002i−2i200-200−2i2i000000000000
χ282222-2-222-2-20000-2-222−2i−2i2i2i0000002i−2i-2002002i−2i000000000000
χ292-2-222-22-22-222-2-200002i−2i2i−2i002i−2i0000000000002−22−2i2−i2i2−i20000
χ302-2-222-22-22-222-2-200002i−2i2i−2i002i−2i000000000000−22−22−i2i2−i2i20000
χ312-2-222-22-22-222-2-20000−2i2i−2i2i00−2i2i0000000000002−22−2−i2i2−i2i20000
χ322-2-222-22-22-222-2-20000−2i2i−2i2i00−2i2i000000000000−22−22i2−i2i2−i20000
χ332-2-222-22-22-2-2-22200002i−2i2i−2i00−2i2i0000000000002−2−22i2−i2−i2i20000
χ342-2-222-22-22-2-2-22200002i−2i2i−2i00−2i2i000000000000−222−2−i2i2i2−i20000
χ352-2-222-22-22-2-2-2220000−2i2i−2i2i002i−2i0000000000002−2−22−i2i2i2−i20000
χ362-2-222-22-22-2-2-2220000−2i2i−2i2i002i−2i000000000000−222−2i2−i2−i2i20000
χ37444444-4-4-4-400004-44-400000000000000000000000000000000
χ38444444-4-4-4-40000-44-4400000000000000000000000000000000
χ394444-4-4-4-44400004-4-4400000000000000000000000000000000
χ404444-4-4-4-4440000-444-400000000000000000000000000000000
χ414-4-444-4-44-4400000000000000004i−4i0000000000000000000000
χ424-4-444-4-44-440000000000000000−4i4i0000000000000000000000
χ434-4-44-444-4-44000000004-4-440000000000000000000000000000
χ444-4-44-444-4-4400000000-444-40000000000000000000000000000
χ454-4-44-44-444-40000000000004-400000000000000000000000000
χ464-4-44-44-444-4000000000000-4400000000000000000000000000
χ4788-8-80000004-44-4000000000000000000000000000000000000
χ4888-8-8000000-44-44000000000000000000000000000000000000
χ498-88-80000004-4-44000000000000000000000000000000000000
χ508-88-8000000-444-4000000000000000000000000000000000000

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