Finite Group Databasebeta

← Group #167010

Character table — Group #167010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422224444488888888888888882444444444448888
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
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-11-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-11-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-11-11-1-11111-1-1
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-111111111-1-1-1-11-11-1-11-1111-1-1-1-111
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-111-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-111-111-1-1-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-11-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-111-1-1-1-111111111-1-1-1-11-1-111-11-1-1-11111-1-1
χ172222222222222222-2-2-22-2-2-222222-20000000000000000000000-2-2000000000000
χ182222222222222222-2-2-22-2-2-22-2-2-2-2-2000000000000000000000022000000000000
χ19222222222222-2-2-2-2222-2-2-22-20000-222220000000000000000-2-200000000000000
χ20222222222222-2-2-2-2222-2-2-22-20000-2-2-2-2-200000000000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2000020000000000000000000000002-2-2200000000
χ22222222222222-2-2-2-2-2-2-2-222-2-200002000000000000000000000000-222-200000000
χ2322222222-2-2-2-222222-2-2-2-2-22-20000222-2-200000000000000002-200000000000000
χ2422222222-2-2-2-222222-2-2-2-2-22-200002-2-2220000000000000000-2200000000000000
χ2522222222-2-2-2-22222-222-222-2-20000-200000000000000000000000022-2-200000000
χ2622222222-2-2-2-22222-222-222-2-20000-2000000000000000000000000-2-22200000000
χ2722222222-2-2-2-2-2-2-2-2-2222-2-2-2222-2-220000000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2222-2-2-22-2-222200000000000000000000002-2000000000000
χ292-222-22-2-222-2-20000-22-200020000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ302-222-22-2-222-2-20000-22-200020000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ312-222-22-2-222-2-20000-22-20002000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ322-222-22-2-222-2-20000-22-20002000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ332-222-22-2-2-2-2220000-2-2200020000002i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ342-222-22-2-2-2-2220000-2-2200020000002i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352-222-22-2-2-2-2220000-2-220002000000−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ362-222-22-2-2-2-2220000-2-220002000000−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-22-2-2-2222-22-222-2-2000-200022-22-2000002−22−22−22−2000000000000000000002−22−2
χ382-22-2-2-2222-22-222-2-2000-200022-22-200000−22−22−22−2200000000000000000000−22−22
χ392-22-2-2-2222-22-222-2-2000-20002-22-22000002−22−22−22−200000000000000000000−22−22
χ402-22-2-2-2222-22-222-2-2000-20002-22-2200000−22−22−22−22000000000000000000002−22−2
χ412-22-2-2-222-22-22-2-222000-200022-2-22000002−22−2−22−22000000000000000000002−2−22
χ422-22-2-2-222-22-22-2-222000-200022-2-2200000−22−222−22−200000000000000000000−222−2
χ432-22-2-2-222-22-22-2-222000-20002-222-2000002−22−2−22−2200000000000000000000−222−2
χ442-22-2-2-222-22-22-2-222000-20002-222-200000−22−222−22−2000000000000000000002−2−22
χ45444-44-4-4-44-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ46444-44-4-4-44-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ47444-44-4-4-4-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ48444-44-4-4-4-444-4000000000000000000000-222-22-2-22000000000000000000000000
χ4944-4-4-444-400004-44-400000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ5044-4-4-444-400004-44-40000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ5144-4-4-444-40000-44-4400000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5244-4-4-444-40000-44-440000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ534-444-44-4-444-4-400004-44000-4000000000000000000000000000000000000000000
χ544-444-44-4-4-4-444000044-4000-4000000000000000000000000000000000000000000
χ554-44-4-4-4444-44-4-4-4440004000-400000000000000000000000000000000000000000
χ564-44-4-4-444-44-4444-4-40004000-400000000000000000000000000000000000000000
χ574-4-444-44-400004-4-44000000000000000000000000000000000000000002i−2i2i−2i0000
χ584-4-444-44-400004-4-4400000000000000000000000000000000000000000−2i2i−2i2i0000
χ594-4-444-44-40000-444-4000000000000000000000000000000000000000002i−2i−2i2i0000
χ604-4-444-44-40000-444-400000000000000000000000000000000000000000−2i2i2i−2i0000
χ614-4-4-444-440000000000004-40000000000000000000000022−22−22220000000000000000
χ624-4-4-444-440000000000004-400000000000000000000000−222222−220000000000000000
χ634-4-4-444-44000000000000-44000000000000000000022−22−222200000000000000000000
χ644-4-4-444-44000000000000-440000000000000000000−222222−2200000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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