Finite Group Databasebeta

← Group #168581

Character table — Group #168581

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222222244444444442222444444444888888882244448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-11-1-11-1-1111111-1-1-111-1-111-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-11-1-1111111-1-1-111-1-111-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-11-1-11-1-1111111-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-11
χ1211111111-1-1-1-11-1-11-1-1111111-1-1-1-1-111-1-111-1-1-1-11111-111-1-11-1-11111-1-11-1
χ1311111111-1-1-1-11-1-11-1-11111-1-111-111-1-1-1-1111111-1-1-1-11-1-11-11-1-11111-1-1-11
χ1411111111-1-1-1-11-1-11-1-11111-1-111-111-1-1-1-111-1-1-1-111111-1-11-1111-1-1-1-1111-1
χ1511111111-1-1-1-11-1-11-1-11111-1-111-1-1-11111-1-11111-1-1-1-1-11-111-1-1-111-1-1111-1
χ1611111111-1-1-1-11-1-11-1-11111-1-111-1-1-11111-1-1-1-1-1-11111-11-111-111-1-111-1-1-11
χ17222222222222222-2-2-2-2-22-20000-22222000000000000-2-200000000000000
χ18222222222222222-2-2-2-2-22-20000-2-2-2-2-20000000000002200000000000000
χ19222222222222-2-2-2222-2-2-222222-2000000000000000000-2-2000000000000
χ20222222222222-2-2-2222-2-2-22-2-2-2-2-200000000000000000022000000000000
χ21222222222222-2-2-2-2-2-222-2-20000200002222000000000000-2-20000000000
χ22222222222222-2-2-2-2-2-222-2-2000020000-2-2-2-2000000000000220000000000
χ2322222222-2-2-2-22-2-2-222-2-22-20000222-2-2000000000000-2200000000000000
χ2422222222-2-2-2-22-2-2-222-2-22-200002-2-2220000000000002-200000000000000
χ2522222222-2-2-2-2-2222-2-2-2-2-2222-2-22000000000000000000-22000000000000
χ2622222222-2-2-2-2-2222-2-2-2-2-22-2-22220000000000000000002-2000000000000
χ2722222222-2-2-2-2-222-22222-2-20000-2000022-2-2000000000000-220000000000
χ2822222222-2-2-2-2-222-22222-2-20000-20000-2-2220000000000002-20000000000
χ292222-2-2-2-222-2-2-22-20000020000002i−2i2i−2i000022−2−222−2−20000000000i2−i2i2−i200
χ302222-2-2-2-222-2-2-22-20000020000002i−2i2i−2i0000−2−222−2−2220000000000−i2i2−i2i200
χ312222-2-2-2-222-2-2-22-2000002000000−2i2i−2i2i000022−2−222−2−20000000000−i2i2−i2i200
χ322222-2-2-2-222-2-2-22-2000002000000−2i2i−2i2i0000−2−222−2−2220000000000i2−i2i2−i200
χ332222-2-2-2-2-2-222-2-220000020000002i−2i−2i2i000022−2−2−2−2220000000000i2−i2−i2i200
χ342222-2-2-2-2-2-222-2-220000020000002i−2i−2i2i0000−2−22222−2−20000000000−i2i2i2−i200
χ352222-2-2-2-2-2-222-2-22000002000000−2i2i2i−2i000022−2−2−2−2220000000000−i2i2i2−i200
χ362222-2-2-2-2-2-222-2-22000002000000−2i2i2i−2i0000−2−22222−2−20000000000i2−i2−i2i200
χ3722-2-2-22-222-22-200022-2000-22-22-2000000000i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2000000
χ3822-2-2-22-222-22-200022-2000-22-22-2000000000−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2000000
χ3922-2-2-22-222-22-200022-2000-2-22-22000000000i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2000000
χ4022-2-2-22-222-22-200022-2000-2-22-22000000000−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2000000
χ4122-2-2-22-22-22-220002-22000-22-2-22000000000i2−i2i2−i2−i2i2−i2i2000000i2−i2−i2i2000000
χ4222-2-2-22-22-22-220002-22000-22-2-22000000000−i2i2−i2i2i2−i2i2−i2000000−i2i2i2−i2000000
χ4322-2-2-22-22-22-220002-22000-2-222-2000000000i2−i2i2−i2−i2i2−i2i2000000−i2i2i2−i2000000
χ4422-2-2-22-22-22-220002-22000-2-222-2000000000−i2i2−i2i2i2−i2i2−i2000000i2−i2−i2i2000000
χ454444-4-4-4-444-4-44-4400000-400000000000000000000000000000000000000
χ464444-4-4-4-4-4-44444-400000-400000000000000000000000000000000000000
χ4744-4-44-44-44-4-44000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ4844-4-44-44-44-4-4400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4944-4-44-44-4-444-4000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5044-4-44-44-4-444-400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5144-4-4-44-444-44-4000-4-4400040000000000000000000000000000000000000
χ5244-4-4-44-44-44-44000-44-400040000000000000000000000000000000000000
χ534-4-44-4-44400000000004-400000000000004-4000000000000000000000000
χ544-4-44-4-44400000000004-40000000000000-44000000000000000000000000
χ554-4-44-4-4440000000000-44000000000004-400000000000000000000000000
χ564-4-44-4-4440000000000-4400000000000-4400000000000000000000000000
χ578-88-88-8-88000000000000000000000000000000000000000000000000000
χ588-88-8-888-8000000000000000000000000000000000000000000000000000
χ598-8-8888-8-8000000000000000000000000000000000000000000000000000

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