Finite Group Databasebeta

← Group #500031

Character table — Group #500031

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122224444444444444888888888888888888888816161616161616161632323232
order12222222244444444444422224444444444444444442444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-11111-1-1-1-1
χ3111111111111111111111-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-11111
χ5111111111111-1-1-1-1111111111-1-111111111-1-1-1-111-1-11-1-11-1-1-1-1-111-1-1
χ6111111111111-1-1-1-1111111111-1-1111111-1-111-1-1-1-111-11-1-11-1-1-1-1-1-111
χ7111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11-1-11-11111-1-111
χ8111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-11-1-11111111-1-1
χ91111-1-111-11-1-111111111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-111-1-11-11-1
χ101111-1-111-11-1-111111111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-11111-1-1-11-11
χ111111-1-111-11-1-1111111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111-11-11
χ121111-1-111-11-1-1111111111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-111-1-1111-11-1
χ131111-1-111-11-1-1-1-1-1-11111111-1-1-1-1-1-111-1-1111111-1-1-1-11-11-11-1-1111-1-11
χ141111-1-111-11-1-1-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1111-1-1-111-111-1
χ151111-1-111-11-1-1-1-1-1-111111-1-111-1-1-1-1-1-111111111-1-1-1-11-11-1111-1-1-111-1
χ161111-1-111-11-1-1-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1111111-1111-111-1-11-1-11
χ172222222222222222-2-2-2-220000-2-2-2-20000000022000000-20000000000
χ18222222222222-2-2-2-2-2-2-2-22000022-2-200000000-2-200000020000000000
χ19222222222-2-2-2000022-2-2-20000002-2000000220000220-200-200000000
χ20222222222-2-2-2000022-2-2-20000002-2000000-2-20000-2-20200200000000
χ21222222222-2-2-20000-2-222-2000000-2200002200002200-200-2000000000
χ22222222222-2-2-20000-2-222-2000000-220000-2-20000-2-2002002000000000
χ232222-2-222-22-2-22222-2-2-2-220000-2-22200000000-2-200000020000000000
χ242222-2-222-22-2-2-2-2-2-2-2-2-2-22000022220000000022000000-20000000000
χ252222-2-222-2-222000022-2-2-2000000-22000000220000-2-20200-200000000
χ262222-2-222-2-222000022-2-2-2000000-22000000-2-20000220-200200000000
χ272222-2-222-2-2220000-2-222-20000002-20000220000-2-200-2002000000000
χ282222-2-222-2-2220000-2-222-20000002-20000-2-200002200200-2000000000
χ292-2-22002-202002i2i−2i−2i2-22-2-2002-22i−2i00002-2000000000000000002i−2i0000
χ302-2-22002-202002i2i−2i−2i2-22-2-200-222i−2i0000-2200000000000000000−2i2i0000
χ312-2-22002-202002i2i−2i−2i-22-22-22-200−2i2i002-2000000000000000002i−2i000000
χ322-2-22002-202002i2i−2i−2i-22-22-2-2200−2i2i00-2200000000000000000−2i2i000000
χ332-2-22002-20200−2i−2i2i2i2-22-2-2002-2−2i2i00002-200000000000000000−2i2i0000
χ342-2-22002-20200−2i−2i2i2i2-22-2-200-22−2i2i0000-22000000000000000002i−2i0000
χ352-2-22002-20200−2i−2i2i2i-22-22-22-2002i−2i002-200000000000000000−2i2i000000
χ362-2-22002-20200−2i−2i2i2i-22-22-2-22002i−2i00-22000000000000000002i−2i000000
χ37444444-4-4-400000000000022220000-2-2-2-200000000000000000000000
χ38444444-4-4-4000000000000-2-2-2-20000222200000000000000000000000
χ394444-4-4-4-4400000000000022-2-20000-2-22200000000000000000000000
χ404444-4-4-4-44000000000000-2-222000022-2-200000000000000000000000
χ414-44-44-40000002i−2i2i−2i000000000000000002i−2i2-22i−2i2i−2i2-20000000000000
χ424-44-44-40000002i−2i2i−2i00000000000000000−2i2i-222i−2i−2i2i-220000000000000
χ434-44-44-4000000−2i2i−2i2i000000000000000002i−2i-22−2i2i2i−2i-220000000000000
χ444-44-44-4000000−2i2i−2i2i00000000000000000−2i2i2-2−2i2i−2i2i2-20000000000000
χ454-44-4-440000002i−2i2i−2i000000000000000002i−2i-22−2i2i−2i2i2-20000000000000
χ464-44-4-440000002i−2i2i−2i00000000000000000−2i2i2-2−2i2i2i−2i-220000000000000
χ474-44-4-44000000−2i2i−2i2i000000000000000002i−2i2-22i−2i−2i2i-220000000000000
χ484-44-4-44000000−2i2i−2i2i00000000000000000−2i2i-222i−2i2i−2i2-20000000000000
χ494-4-44004-40-40000004-4-44400000000000000000000000000000000000
χ504-4-44004-40-4000000-444-4400000000000000000000000000000000000
χ514-4-4400-44004-40000000002-22-20000-22-2200000000000000000000000
χ524-4-4400-44004-4000000000-22-2200002-22-200000000000000000000000
χ534-4-4400-4400-440000000002-2-220000-222-200000000000000000000000
χ544-4-4400-4400-44000000000-222-200002-2-2200000000000000000000000
χ5588-8-8000000004-4-440000000000000000000000000000000000000000
χ5688-8-800000000-444-40000000000000000000000000000000000000000

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