Finite Group Databasebeta

← Group #457241

Character table — Group #457241

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222222244448888888888888888881616161616161616161616161616161616161616
order12222222222244444444888844444444888888888822244444444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11111-111-1-111-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-111-1-11-1-1-1-1111111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1111111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-11111-1-11-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-111-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-111-1-111-1-111
χ1722222222-2-2-2-222-22-2-2-22000022-2-2000000000022-2-2200000000-20000000000
χ1822222222-2-2-2-222-22-2-2-22000022-2-20000000000-2-222-20000000020000000000
χ1922222222-2-2-2-222-22-2-2-220000-2-222000000000022-2-2-20000000020000000000
χ2022222222-2-2-2-222-22-2-2-220000-2-2220000000000-2-222200000000-20000000000
χ2122222222-2-2-2-2-2-22-2222-2222200000000-2-2000000000002-2002-200000000000
χ2222222222-2-2-2-2-2-22-2222-2222200000000-2-200000000000-2200-2200000000000
χ2322222222-2-2-2-2-2-22-2222-2-2-2-2-20000000022000000000002-200-2200000000000
χ2422222222-2-2-2-2-2-22-2222-2-2-2-2-2000000002200000000000-22002-200000000000
χ2522-2-22-2-2222-2-222-2-222-2-222-2-22i−2i2i−2i00002-22i2i−2i−2i000000000000000000000000
χ2622-2-22-2-2222-2-222-2-222-2-222-2-2−2i2i−2i2i00002-2−2i−2i2i2i000000000000000000000000
χ2722-2-22-2-2222-2-222-2-222-2-2-2-2222i−2i2i−2i0000-22−2i−2i2i2i000000000000000000000000
χ2822-2-22-2-2222-2-222-2-222-2-2-2-222−2i2i−2i2i0000-222i2i−2i−2i000000000000000000000000
χ2922-2-22-2-22-2-222222-2-2-22-200002i−2i−2i2i22-2-20000000000000000000000002i−2i0000
χ3022-2-22-2-22-2-222222-2-2-22-200002i−2i−2i2i-2-222000000000000000000000000−2i2i0000
χ3122-2-22-2-22-2-222222-2-2-22-20000−2i2i2i−2i22-2-2000000000000000000000000−2i2i0000
χ3222-2-22-2-22-2-222222-2-2-22-20000−2i2i2i−2i-2-2220000000000000000000000002i−2i0000
χ3322-2-22-2-22-2-222-2-2-2222-2222-2-200000000-220000000002-2002-20000000000000
χ3422-2-22-2-22-2-222-2-2-2222-2222-2-200000000-22000000000-2200-220000000000000
χ3522-2-22-2-22-2-222-2-2-2222-22-2-222000000002-20000000002-200-220000000000000
χ3622-2-22-2-22-2-222-2-2-2222-22-2-222000000002-2000000000-22002-20000000000000
χ372-222-2-2-222-22-22-2222-2-2-2000000000000002i−2i2i−2i00000000000000002-2002i−2i00
χ382-222-2-2-222-22-22-2222-2-2-2000000000000002i−2i2i−2i0000000000000000-2200−2i2i00
χ392-222-2-2-222-22-22-2222-2-2-200000000000000−2i2i−2i2i00000000000000002-200−2i2i00
χ402-222-2-2-222-22-22-2222-2-2-200000000000000−2i2i−2i2i0000000000000000-22002i−2i00
χ412-2-2-2-22222-2-222-2-2-22-222000000000000002-2-22000000000000002-20000002-2
χ422-2-2-2-22222-2-222-2-2-22-222000000000000002-2-2200000000000000-22000000-22
χ432-2-2-2-22222-2-222-2-2-22-22200000000000000-222-2000000000000002-2000000-22
χ442-2-2-2-22222-2-222-2-2-22-22200000000000000-222-200000000000000-220000002-2
χ45444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000
χ4644-4-44-4-4444-4-4-4-444-4-444000000000000000000000000000000000000000000
χ474-444-4-4-444-44-4-44-4-4-4444000000000000000000000000000000000000000000
χ484-444-4-4-44-44-444-4-44-444-4000000000000000000000000000000000000000000
χ494-444-4-4-44-44-44-444-44-4-44000000000000000000000000000000000000000000
χ504-44-444-4-400000000000022−2222−2200002i−2i2i−2i000000002i2−2i200000000000000000000
χ514-44-444-4-400000000000022−2222−220000−2i2i−2i2i00000000−2i22i200000000000000000000
χ524-44-444-4-4000000000000−2222−222200002i−2i2i−2i00000000−2i22i200000000000000000000
χ534-44-444-4-4000000000000−2222−22220000−2i2i−2i2i000000002i2−2i200000000000000000000
χ544-4-444-44-400000000000022−22−222200002i−2i−2i2i0000002i2−2i20000000000000000000000
χ554-4-444-44-400000000000022−22−22220000−2i2i2i−2i000000−2i22i20000000000000000000000
χ564-4-444-44-4000000000000−222222−2200002i−2i−2i2i000000−2i22i20000000000000000000000
χ574-4-444-44-4000000000000−222222−220000−2i2i2i−2i0000002i2−2i20000000000000000000000
χ584-4-4-4-44444-4-44-4444-44-4-4000000000000000000000000000000000000000000
χ594-4-4-4-4444-444-44-44-4-44-44000000000000000000000000000000000000000000
χ604-4-4-4-4444-444-4-44-444-44-4000000000000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-88-88-8-8000000000000000000000000000000000000000000000000000000

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