Finite Group Databasebeta

← Group #170798

Character table — Group #170798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444244448888888822244444448888888844
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-11-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-111111111-11-11-11-11-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-111111111-1-11-1-1-11-111-1-1-1-11111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-111111111-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1111111-1-1-1-111
χ911111111-1-1-1-1-1-1111111-111-1-11111-1-1-1-111-11-1-1-1-11111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1111111-111-1-11111-1-1-1-11-11-1-1111-1-111-1-1-1-111-11
χ1111111111-1-1-1-1-1-1111111-111-1-1-1-1-1-1111111-11-1-1-1-111-1-111-1-111-11
χ1211111111-1-1-1-1-1-1111111-111-1-1-1-1-1-111111-11-1-1111-1-1-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-11111-11-1-1-1-1-111-1-1111-1
χ1411111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-11111-1-1-11
χ1511111111-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-11111-11-1-1-111-1-111-1-1-11
χ1611111111-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-111-111111-1-1-1-1111-1
χ17222222222222-2-2-2-222-2-2-2000000000000002000-202-20000000000
χ18222222222222-2-2-2-222-2-2-200000000000000-200020-220000000000
χ192222222222-2-222-2-2-2-222-2222200000000-2000-2000000000000000
χ202222222222-2-222-2-2-2-222-2-2-2-2-20000000020002000000000000000
χ212222222222-2-2-2-222-2-2-2-22000000000000020-20-202000000000000
χ222222222222-2-2-2-222-2-2-2-220000000000000-202020-2000000000000
χ2322222222-2-2222222-2-2-2-2-2000000000000020-2020-2000000000000
χ2422222222-2-2222222-2-2-2-2-20000000000000-2020-202000000000000
χ2522222222-2-222-2-2-2-2-2-222222-2-200000000-20002000000000000000
χ2622222222-2-222-2-2-2-2-2-2222-2-222000000002000-2000000000000000
χ2722222222-2-2-2-222-2-222-2-22000000000000002000-20-220000000000
χ2822222222-2-2-2-222-2-222-2-2200000000000000-2000202-20000000000
χ29222-2-22-2-22i−2i002i−2i00002-202i−2i2-2i2i2−i2−i222−2−200000000002−2i2−i2000000
χ30222-2-22-2-22i−2i002i−2i00002-202i−2i2-2−i2−i2i2i2−2−2220000000000−22−i2i2000000
χ31222-2-22-2-22i−2i002i−2i00002-20−2i2i-22i2i2−i2−i222−2−20000000000−22−i2i2000000
χ32222-2-22-2-22i−2i002i−2i00002-20−2i2i-22−i2−i2i2i2−2−22200000000002−2i2−i2000000
χ33222-2-22-2-2−2i2i00−2i2i00002-202i−2i-22i2i2−i2−i2−2−22200000000002−2−i2i2000000
χ34222-2-22-2-2−2i2i00−2i2i00002-202i−2i-22−i2−i2i2i222−2−20000000000−22i2−i2000000
χ35222-2-22-2-2−2i2i00−2i2i00002-20−2i2i2-2i2i2−i2−i2−2−2220000000000−22i2−i2000000
χ36222-2-22-2-2−2i2i00−2i2i00002-20−2i2i2-2−i2−i2i2i222−2−200000000002−2−i2i2000000
χ37444-4-44-4-44i−4i00−4i4i0000-44000000000000000000000000000000000
χ38444-4-44-4-4−4i4i004i−4i0000-44000000000000000000000000000000000
χ3944-44-4-44-4004i−4i00000000000002-22-22i−2i2i−2i00000000000000000000
χ4044-44-4-44-4004i−4i0000000000000-22-22−2i2i−2i2i00000000000000000000
χ4144-44-4-44-400−4i4i00000000000002-22-2−2i2i−2i2i00000000000000000000
χ4244-44-4-44-400−4i4i0000000000000-22-222i−2i2i−2i00000000000000000000
χ4344-4-44-4-44000000004-4000000000002i2−2i2−2i22i200000000000000000000
χ4444-4-44-4-44000000004-400000000000−2i22i22i2−2i200000000000000000000
χ4544-4-44-4-4400000000-4400000002i2−2i2−2i22i2000000000000000000000000
χ4644-4-44-4-4400000000-440000000−2i22i22i2−2i2000000000000000000000000
χ474-4444-4-4-40000004-400000000000000000000000000000002i2−2i20000
χ484-4444-4-4-40000004-40000000000000000000000000000000−2i22i20000
χ494-4444-4-4-4000000-440000000000000000000000000000000002i2−2i200
χ504-4444-4-4-4000000-44000000000000000000000000000000000−2i22i200
χ518-88-8-8-888000000000000000000000000000000000000000000000
χ528-8-88-88-88000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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