Finite Group Databasebeta

← Group #167166

Character table — Group #167166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422224444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
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
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111-1-111111-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11111-1-11-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111-1-111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111-111-1-111
χ1211111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1111-1-1111-1-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111-1-1111-1-111-111-1-11111-1-1-1-1-1-1-1-111111-111-1-111-11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111-1-1111-1-111-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-111-111111-1-1
χ1511111111-1-1-1-1-1-1-1-1111-1-1111-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111-1-1-111111-1-1
χ1611111111-1-1-1-1-1-1-1-1111-1-1111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-111111-1-1-11-1-1-1-111
χ172222222222222222-22-2-2-2-22-20000-222220000000000000000-2-200000000000000
χ182222222222222222-22-2-2-2-22-20000-2-2-2-2-200000000000000002200000000000000
χ19222222222222-2-2-2-22-2-2-2-22-2-2000020000000000000000000000002-22-200000000
χ20222222222222-2-2-2-22-2-2-2-22-2-200002000000000000000000000000-22-2200000000
χ21222222222222-2-2-2-2-2-2222-2-222222-20000000000000000000000000000-2-2000000
χ22222222222222-2-2-2-2-2-2222-2-22-2-2-2-2-2000000000000000000000000000022000000
χ2322222222-2-2-2-222222-2-2222-2-20000-20000000000000000000000002-2-2200000000
χ2422222222-2-2-2-222222-2-2222-2-20000-2000000000000000000000000-222-200000000
χ2522222222-2-2-2-22222-2-22-2-2-2-2222-2-220000000000000000000000000000-22000000
χ2622222222-2-2-2-22222-2-22-2-2-2-22-2-222200000000000000000000000000002-2000000
χ2722222222-2-2-2-2-2-2-2-2-22-222-22-20000222-2-20000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2-22-222-22-200002-2-22200000000000000002-200000000000000
χ292-2-222-2-2222-2-222-2-2020000-20000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000000000002−22−2
χ302-2-222-2-2222-2-222-2-2020000-20000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2000000000000−22−22
χ312-2-222-2-2222-2-222-2-2020000-2000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2000000000000−22−22
χ322-2-222-2-2222-2-222-2-2020000-2000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000000000002−22−2
χ332-2-222-2-22-2-222-2-222020000-20000002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i20000000000002−2−22
χ342-2-222-2-22-2-222-2-222020000-20000002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i2000000000000−222−2
χ352-2-222-2-22-2-222-2-222020000-2000000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i2000000000000−222−2
χ362-2-222-2-22-2-222-2-222020000-2000000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i20000000000002−2−22
χ372-2-22-222-22-22-200000022-200-22-22-200000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-22-222-22-22-200000022-200-22-22-200000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-22-222-22-22-200000022-200-2-22-2200000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-22-222-22-22-200000022-200-2-22-2200000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-22-222-2-22-220000002-2200-22-2-2200000i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-2-22-222-2-22-220000002-2200-22-2-2200000−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-2-22-222-2-22-220000002-2200-2-222-200000i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ442-2-22-222-2-22-220000002-2200-2-222-200000−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ454444-4-4-4-44-4-44000000000000000000000000000002-2-222-2-220000000000000000
χ464444-4-4-4-44-4-4400000000000000000000000000000-222-2-222-20000000000000000
χ474444-4-4-4-4-444-4000000000000000000000000000002-2-22-222-20000000000000000
χ484444-4-4-4-4-444-400000000000000000000000000000-222-22-2-220000000000000000
χ4944-4-444-4-400004i−4i4i−4i000000000000000000000000000000000002-20000002i−2i0000
χ5044-4-444-4-400004i−4i4i−4i00000000000000000000000000000000000-22000000−2i2i0000
χ5144-4-444-4-40000−4i4i−4i4i000000000000000000000000000000000002-2000000−2i2i0000
χ5244-4-444-4-40000−4i4i−4i4i00000000000000000000000000000000000-220000002i−2i0000
χ5344-4-4-4-4440000000040000-4000000000002i2−2i22i2−2i20000000000000000000000000000
χ5444-4-4-4-4440000000040000-400000000000−2i22i2−2i22i20000000000000000000000000000
χ5544-4-4-4-44400000000-40000400000000000000022−2222−22000000000000000000000000
χ5644-4-4-4-44400000000-400004000000000000000−2222−2222000000000000000000000000
χ574-44-44-44-400004i−4i−4i4i000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ584-44-44-44-400004i−4i−4i4i00000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ594-44-44-44-40000−4i4i4i−4i000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ604-44-44-44-40000−4i4i4i−4i00000000000000000-222-22i−2i−2i2i000000000000000000000000
χ614-4-444-4-4444-4-4-4-4440-400004000000000000000000000000000000000000000000
χ624-4-444-4-44-4-44444-4-40-400004000000000000000000000000000000000000000000
χ634-4-44-444-44-44-4000000-4-4400400000000000000000000000000000000000000000
χ644-4-44-444-4-44-44000000-44-400400000000000000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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