Finite Group Databasebeta

← Group #167390

Character table — Group #167390

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-111-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-111-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-11-1-11-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1-111-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-11-11-1-111-1-1-11111-1-1
χ1722222222222222222-2-2-2-2-22-200-200222200000000000000000000-2-20000000000
χ1822222222222222222-2-2-2-2-22-200-200-2-2-2-200000000000000000000220000000000
χ19222222222222-2-2-2-2-2222-2-2-2222-2220000000000000000000000-2-2000000000000
χ20222222222222-2-2-2-2-2222-2-2-22-2-2-2-2-2000000000000000000000022000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-200200000000000000000000002-20000-2200000000
χ22222222222222-2-2-2-2-2-2-2-222-2-20020000000000000000000000-2200002-200000000
χ2322222222-2-2-2-22222-22-2-2-2-2-22222-2-200000000000000000000002-2000000000000
χ2422222222-2-2-2-22222-22-2-2-2-2-22-2-22220000000000000000000000-22000000000000
χ2522222222-2-2-2-22222-2-22222-2-200-20000000000000000000000220000-2-200000000
χ2622222222-2-2-2-22222-2-22222-2-200-20000000000000000000000-2-200002200000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-20020022-2-200000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-200200-2-222000000000000000000002-20000000000
χ2922-2-2-222-222-2-20000022-2000-22-202-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3022-2-2-222-222-2-20000022-2000-22-202-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3122-2-2-222-222-2-20000022-2000-2-220-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3222-2-2-222-222-2-20000022-2000-2-220-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3322-2-2-222-2-2-222000002-22000-22-20-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ3422-2-2-222-2-2-222000002-22000-22-20-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ3522-2-2-222-2-2-222000002-22000-2-2202-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ3622-2-2-222-2-2-222000002-22000-2-2202-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-22-2-22-222-22-222-2-2200000-20000002i−2i2i−2i2−22−22−22−200000000000000000000i2−i2i2−i2
χ382-22-2-22-222-22-222-2-2200000-20000002i−2i2i−2i−22−22−22−2200000000000000000000−i2i2−i2i2
χ392-22-2-22-222-22-222-2-2200000-2000000−2i2i−2i2i2−22−22−22−200000000000000000000−i2i2−i2i2
χ402-22-2-22-222-22-222-2-2200000-2000000−2i2i−2i2i−22−22−22−2200000000000000000000i2−i2i2−i2
χ412-22-2-22-22-22-22-2-222200000-20000002i−2i−2i2i2−22−2−22−2200000000000000000000i2−i2−i2i2
χ422-22-2-22-22-22-22-2-222200000-20000002i−2i−2i2i−22−222−22−200000000000000000000−i2i2i2−i2
χ432-22-2-22-22-22-22-2-222200000-2000000−2i2i2i−2i2−22−2−22−2200000000000000000000−i2i2i2−i2
χ442-22-2-22-22-22-22-2-222200000-2000000−2i2i2i−2i−22−222−22−200000000000000000000i2−i2−i2i2
χ454444-4-4-4-400004-44-400000000000000000000000002-22-22-22-20000000000000000
χ464444-4-4-4-400004-44-40000000000000000000000000-22-22-22-220000000000000000
χ474444-4-4-4-40000-44-4400000000000000000000000002-22-2-22-220000000000000000
χ484444-4-4-4-40000-44-440000000000000000000000000-22-222-22-20000000000000000
χ4944-4-44-4-440000000000004-4000000000000000000000002i2−2i2−2i22i20000000000000000
χ5044-4-44-4-440000000000004-400000000000000000000000−2i22i22i2−2i20000000000000000
χ5144-4-44-4-44000000000000-4400000000000000000002i2−2i2−2i22i200000000000000000000
χ5244-4-44-4-44000000000000-440000000000000000000−2i22i22i2−2i200000000000000000000
χ5344-4-4-444-444-4-400000-4-44000400000000000000000000000000000000000000000
χ5444-4-4-444-4-4-44400000-44-4000400000000000000000000000000000000000000000
χ554-44-44-44-400004-4-44000000000000000000000000000000000000000002i−2i2i−2i0000
χ564-44-44-44-400004-4-4400000000000000000000000000000000000000000−2i2i−2i2i0000
χ574-44-44-44-40000-444-4000000000000000000000000000000000000000002i−2i−2i2i0000
χ584-44-44-44-40000-444-400000000000000000000000000000000000000000−2i2i2i−2i0000
χ594-44-4-44-444-44-4-4-444-4000004000000000000000000000000000000000000000000
χ604-44-4-44-44-44-4444-4-4-4000004000000000000000000000000000000000000000000
χ614-4-4444-4-44-4-440000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ624-4-4444-4-44-4-44000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ634-4-4444-4-4-444-40000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ644-4-4444-4-4-444-4000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ658-8-88-8-888000000000000000000000000000000000000000000000000000000000

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