Finite Group Databasebeta

← Group #507943

Character table — Group #507943

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1244222444888844444444884488888822444444888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-11-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-1-1-111-1-11-11-11111-1-1-1-1-1-111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-111-1-1-11-11-1-1-1-1111111-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-1-1
χ1011111111111111-1-1-1-1111111-1-1-1-1-1-1111-11-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-111-11-111111-1-1-1-111-1-1-1-111-1-111
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1111-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ172222222222-2-2-2-222222222-2-222-2-2-2-2-2-2000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000
χ2122-2-22-2-2-22200002i2i−2i−2i2i2i−2i−2i002-200000000000000000000002−2i2−i2i2−i22−2
χ2222-2-22-2-2-22200002i2i−2i−2i2i2i−2i−2i002-20000000000000000000000−22−i2i2−i2i2−22
χ2322-2-22-2-2-22200002i2i−2i−2i−2i−2i2i2i00-2200000000000000000000002−2i2−i2−i2i2−22
χ2422-2-22-2-2-22200002i2i−2i−2i−2i−2i2i2i00-220000000000000000000000−22−i2i2i2−i22−2
χ2522-2-22-2-2-2220000−2i−2i2i2i2i2i−2i−2i00-2200000000000000000000002−2−i2i2i2−i2−22
χ2622-2-22-2-2-2220000−2i−2i2i2i2i2i−2i−2i00-220000000000000000000000−22i2−i2−i2i22−2
χ2722-2-22-2-2-2220000−2i−2i2i2i−2i−2i2i2i002-200000000000000000000002−2−i2i2−i2i22−2
χ2822-2-22-2-2-2220000−2i−2i2i2i−2i−2i2i2i002-20000000000000000000000−22i2−i2i2−i2−22
χ2922-2-2-22-222-222-2-200002i−2i2i−2i2-20000002i−2i00002-20000002i−2i0000000000
χ3022-2-2-22-222-222-2-200002i−2i2i−2i2-20000002i−2i0000-22000000−2i2i0000000000
χ3122-2-2-22-222-222-2-20000−2i2i−2i2i2-2000000−2i2i00002-2000000−2i2i0000000000
χ3222-2-2-22-222-222-2-20000−2i2i−2i2i2-2000000−2i2i0000-220000002i−2i0000000000
χ3322-2-2-22-222-2-2-22200002i−2i2i−2i-22000000−2i2i20-2000002i−2i00000000000000
χ3422-2-2-22-222-2-2-22200002i−2i2i−2i-22000000−2i2i-20200000−2i2i00000000000000
χ3522-2-2-22-222-2-2-2220000−2i2i−2i2i-220000002i−2i20-200000−2i2i00000000000000
χ3622-2-2-22-222-2-2-2220000−2i2i−2i2i-220000002i−2i-202000002i−2i00000000000000
χ3722-2-2-2-222-2222-2-22i−2i2i−2i0000-2200002i−2i000000002-20000002i−2i00000000
χ3822-2-2-2-222-2222-2-22i−2i2i−2i0000-2200002i−2i00000000-22000000−2i2i00000000
χ3922-2-2-2-222-2222-2-2−2i2i−2i2i0000-220000−2i2i000000002-2000000−2i2i00000000
χ4022-2-2-2-222-2222-2-2−2i2i−2i2i0000-220000−2i2i00000000-220000002i−2i00000000
χ4122-2-2-2-222-22-2-2222i−2i2i−2i00002-20000−2i2i00020-20000002i−2i000000000000
χ4222-2-2-2-222-22-2-2222i−2i2i−2i00002-20000−2i2i000-202000000−2i2i000000000000
χ4322-2-2-2-222-22-2-222−2i2i−2i2i00002-200002i−2i00020-2000000−2i2i000000000000
χ4422-2-2-2-222-22-2-222−2i2i−2i2i00002-200002i−2i000-2020000002i−2i000000000000
χ4544444-4-44-4-4444400000000-4-400000000000000000000000000000000
χ4644444-4-44-4-4-4-4-4-4000000004400000000000000000000000000000000
χ474444-44-4-4-4400004-4-4400000000000000000000000000000000000000
χ484444-44-4-4-440000-444-400000000000000000000000000000000000000
χ494444-4-44-44-4000000004-4-440000000000000000000000000000000000
χ504444-4-44-44-400000000-444-40000000000000000000000000000000000
χ5144-4-4444-4-4-400000000000000004i−4i0000000000000000000000000000
χ5244-4-4444-4-4-40000000000000000−4i4i0000000000000000000000000000
χ538-88i−8i0000004i2−4i242−42000000000000000000000000000000000000000000
χ548-88i−8i000000−4i24i2−4242000000000000000000000000000000000000000000
χ558-8−8i8i0000004i2−4i2−4242000000000000000000000000000000000000000000
χ568-8−8i8i000000−4i24i242−42000000000000000000000000000000000000000000

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