Finite Group Databasebeta

← Group #98348

Character table — Group #98348

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222244444244444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1111-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1111-1-1111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-11-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1111ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1111−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2-2-2220022-200-2-220000-2000000000000000000
χ18222222222222-2-2-2-2-2-22200-2-2-20022-200002000000000000000000
χ19222222222-2-2-22222-2-22-22200-2-2-20002-2000000000000000000000
χ20222222222-2-2-22222-2-22-2-2-200-222000-22000000000000000000000
χ21222222222-2-2-2-2-2-2-2222-20000200000002-202-20000000000000000
χ22222222222-2-2-2-2-2-2-2222-2000020000000-220-220000000000000000
χ2322222222-22-2-222-2-222-222200-2-2-2000-22000000000000000000000
χ2422222222-22-2-222-2-222-22-2-200-2220002-2000000000000000000000
χ2522222222-22-2-2-2-222-2-2-220000200000002-20-220000000000000000
χ2622222222-22-2-2-2-222-2-2-22000020000000-2202-20000000000000000
χ2722222222-2-222-2-22222-2-20022-20022-20000-2000000000000000000
χ2822222222-2-222-2-22222-2-200-2-2-200-2-2200002000000000000000000
χ29222-2-2-22-2002-2002i−2i2i−2i00002-20002i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ30222-2-2-22-2002-2002i−2i2i−2i00002-20002i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ31222-2-2-22-2002-2002i−2i2i−2i0000-22000−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ32222-2-2-22-2002-2002i−2i2i−2i0000-22000−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ33222-2-2-22-2002-200−2i2i−2i2i00002-2000−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ34222-2-2-22-2002-200−2i2i−2i2i00002-2000−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ35222-2-2-22-2002-200−2i2i−2i2i0000-220002i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ36222-2-2-22-2002-200−2i2i−2i2i0000-220002i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ37444-4-4-44-400-44004i−4i−4i4i00000000000000000000000000000000000
χ38444-4-4-44-400-4400−4i4i4i−4i00000000000000000000000000000000000
χ3944-444-4-4-404000000000-4000000000000000002-22-2000000000000
χ4044-444-4-4-404000000000-400000000000000000-22-22000000000000
χ4144-444-4-4-40-40000000004000000000000000002i−2i−2i2i000000000000
χ4244-444-4-4-40-4000000000400000000000000000−2i2i2i−2i000000000000
χ434-444-44-4-44000000000-400000000000000000000002-22-200000000
χ444-444-44-4-44000000000-40000000000000000000000-22-2200000000
χ454-444-44-4-4-4000000000400000000000000000000002i−2i−2i2i00000000
χ464-444-44-4-4-400000000040000000000000000000000−2i2i2i−2i00000000
χ474-4-44-4-44400004-4000000000004-400000000000000000000000000
χ484-4-44-4-44400004-400000000000-4400000000000000000000000000
χ494-4-44-4-4440000-440000004-40000000000000000000000000000000
χ504-4-44-4-4440000-44000000-440000000000000000000000000000000
χ5188-8-8-88-88000000000000000000000000000000000000000000000
χ528-88-88-8-88000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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