Finite Group Databasebeta

← Group #176539

Character table — Group #176539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222224444444422444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-11-1-1-1-1-11111-1-1-1-11111-1-1
χ4111111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1-1-1111111-1-1-111-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-111-1-1-1-1-11-1-1-11111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1-11-1-1-1111-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-111-1-1-1111-11-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-111-1-1-1111-11-1-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-1-1-1-1-111-1-11-11-11111-1-1-1-11111-1-1-11
χ1211111111-1-1-1-111111111-1-1-1-1-1-111-1-11-11-111-1-11111-1-1-1-1111-1
χ1311111111-1-1-1-1111111-1-111-1-111-1-11-1-11-1-11111-1-111-1-1-1-111-11
χ1411111111-1-1-1-1111111-1-111-1-111-1-11-1-11-1-111-1-111-1-11111-1-11-1
χ1511111111-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-11
χ17222222222222-222-2-2-22222-2-20000-20-20000000000000000000
χ18222222222222-222-2-2-2-2-2-2-2-2-200002020000000000000000000
χ192222222222-2-22-2-2-2-2200002-222-2-2000-2200000000000000000
χ202222222222-2-22-2-2-2-2200002-2-2-2220002-200000000000000000
χ212222222222-2-2-2-2-222-20000-22000002000-22-200000000000000
χ222222222222-2-2-2-2-222-20000-2200000-20002-2200000000000000
χ2322222222-2-2222-2-2-2-220000-222222000-2-200000000000000000
χ2422222222-2-2222-2-2-2-220000-22-2-2-2-20002200000000000000000
χ2522222222-2-222-2-2-222-200002-2000002000-2-2200000000000000
χ2622222222-2-222-2-2-222-200002-200000-200022-200000000000000
χ2722222222-2-2-2-2-222-2-2-222-2-222000020-20000000000000000000
χ2822222222-2-2-2-2-222-2-2-2-2-222220000-2020000000000000000000
χ294444-4-4-4-4000004-4000004-40000000000000000000000000000
χ304444-4-4-4-4000004-400000-440000000000000000000000000000
χ314444-4-4-4-400000-440004-4000000000000000000000000000000
χ324444-4-4-4-400000-44000-44000000000000000000000000000000
χ3344-4-4-444-400000004-4000000000000000000000000000002i2−2i200
χ3444-4-4-444-400000004-400000000000000000000000000000−2i22i200
χ3544-4-4-444-40000000-440000000000000000000000000002i2−2i20000
χ3644-4-4-444-40000000-44000000000000000000000000000−2i22i20000
χ374-44-444-4-4004i−4i0000000000000000000000002-22i−2i0000000000
χ384-44-444-4-4004i−4i000000000000000000000000-22−2i2i0000000000
χ394-44-444-4-400−4i4i0000000000000000000000002-2−2i2i0000000000
χ404-44-444-4-400−4i4i000000000000000000000000-222i−2i0000000000
χ414-44-4-4-444000040000-40000004i−4i000000000000000000000000
χ424-44-4-4-444000040000-4000000−4i4i000000000000000000000000
χ434-44-4-4-4440000-400004000000004-40000000000000000000000
χ444-44-4-4-4440000-40000400000000-440000000000000000000000
χ454-4-444-44-44-40000000000000000000000000000002i−2i2i−2i000000
χ464-4-444-44-44-4000000000000000000000000000000−2i2i−2i2i000000
χ474-4-444-44-4-440000000000000000000000000000002i−2i−2i2i000000
χ484-4-444-44-4-44000000000000000000000000000000−2i2i2i−2i000000
χ4988-8-88-8-88000000000000000000000000000000000000000000
χ508-8-88-88-88000000000000000000000000000000000000000000

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