Finite Group Databasebeta

← Group #458598

Character table — Group #458598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222888888888888888888888888161616161616161616161616161616161616
order12222222222244444444224444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-11-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1111111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1111111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-11111-1-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-1111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111111-1-111
χ1722222222-2-2-2-222-22-2-2-22000022-2-200000000000022-2-22-20000000000000000
χ1822222222-2-2-2-222-22-2-2-22000022-2-2000000000000-2-222-220000000000000000
χ1922222222-2-2-2-222-22-2-2-220000-2-22200000000000022-2-2-220000000000000000
χ2022222222-2-2-2-222-22-2-2-220000-2-222000000000000-2-2222-20000000000000000
χ2122222222-2-2-2-2-2-22-2222-222-2-200000000000022-2-20000000020000-200000000
χ2222222222-2-2-2-2-2-22-2222-222-2-2000000000000-2-22200000000-20000200000000
χ2322222222-2-2-2-2-2-22-2222-2-2-22200000000000022-2-200000000-20000200000000
χ2422222222-2-2-2-2-2-22-2222-2-2-222000000000000-2-2220000000020000-200000000
χ2522-2-222-2-222-2-2222-22-2-2-22-22-200000000000000000000002-2000000002-20000
χ2622-2-222-2-222-2-2222-22-2-2-22-22-20000000000000000000000-2200000000-220000
χ2722-2-222-2-222-2-2222-22-2-2-2-22-2200000000000000000000002-200000000-220000
χ2822-2-222-2-222-2-2222-22-2-2-2-22-220000000000000000000000-22000000002-20000
χ2922-2-222-2-222-2-2-2-2-22-222200002i−2i2i−2i0000000000000000000002i−2i00000002-200
χ3022-2-222-2-222-2-2-2-2-22-222200002i−2i2i−2i000000000000000000000−2i2i0000000-2200
χ3122-2-222-2-222-2-2-2-2-22-22220000−2i2i−2i2i0000000000000000000002i−2i0000000-2200
χ3222-2-222-2-222-2-2-2-2-22-22220000−2i2i−2i2i000000000000000000000−2i2i00000002-200
χ3322-2-222-2-2-2-222-2-2222-2-222-2-222i−2i−2i2i2i2i−2i−2i000000000000000000000000000000
χ3422-2-222-2-2-2-222-2-2222-2-222-2-22−2i2i2i−2i−2i−2i2i2i000000000000000000000000000000
χ3522-2-222-2-2-2-222-2-2222-2-22-222-22i−2i−2i2i−2i−2i2i2i000000000000000000000000000000
χ3622-2-222-2-2-2-222-2-2222-2-22-222-2−2i2i2i−2i2i2i−2i−2i000000000000000000000000000000
χ372-2222-2-2-22-2-222-2-2-222-22000000002i−2i2i−2i22-2-20000000000000002i−2i000000000
χ382-2222-2-2-22-2-222-2-2-222-22000000002i−2i2i−2i-2-222000000000000000−2i2i000000000
χ392-2222-2-2-22-2-222-2-2-222-2200000000−2i2i−2i2i22-2-2000000000000000−2i2i000000000
χ402-2222-2-2-22-2-222-2-2-222-2200000000−2i2i−2i2i-2-2220000000000000002i−2i000000000
χ412-2-2-22-222-22-22-22-2-22-222000000002-2-2200000000000000000000002-200002-2
χ422-2-2-22-222-22-22-22-2-22-222000000002-2-220000000000000000000000-220000-22
χ432-2-2-22-222-22-22-22-2-22-22200000000-222-200000000000000000000002-20000-22
χ442-2-2-22-222-22-22-22-2-22-22200000000-222-20000000000000000000000-2200002-2
χ45444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000
χ46444-4-4-4-440000000000000000000000002-22-22i2−2i200002i2−2i2000000000000000000
χ47444-4-4-4-440000000000000000000000002-22-2−2i22i20000−2i22i2000000000000000000
χ48444-4-4-4-44000000000000000000000000-22-222i2−2i20000−2i22i2000000000000000000
χ49444-4-4-4-44000000000000000000000000-22-22−2i22i200002i2−2i2000000000000000000
χ5044-4-444-4-4-4-44444-4-4-444-4000000000000000000000000000000000000000000
χ514-4444-4-4-44-4-44-4444-4-44-4000000000000000000000000000000000000000000
χ524-4444-4-4-4-444-44-44-4-4-444000000000000000000000000000000000000000000
χ534-4444-4-4-4-444-4-44-4444-4-4000000000000000000000000000000000000000000
χ544-44-4-444-40000000000000000000000002-2-22002i2−2i22i2−2i200000000000000000000
χ554-44-4-444-40000000000000000000000002-2-2200−2i22i2−2i22i200000000000000000000
χ564-44-4-444-4000000000000000000000000-222-2002i2−2i2−2i22i200000000000000000000
χ574-44-4-444-4000000000000000000000000-222-200−2i22i22i2−2i200000000000000000000
χ584-4-4-44-4444-44-44-4-444-44-4000000000000000000000000000000000000000000
χ594-4-4-44-4444-44-4-444-4-44-44000000000000000000000000000000000000000000
χ604-4-4-44-444-44-444-444-44-4-4000000000000000000000000000000000000000000
χ6188-88-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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