Finite Group Databasebeta

← Group #98334

Character table — Group #98334

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222244444222444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1111-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-111-1-11111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-1-1-11-1-1-111-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-11-1-1-111-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-11111111-1-1-111-1-11-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-11111111-1-1-111-1-11-1-1−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
χ1311111111-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111111ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111111−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2-2-222002200-2-2-220000-2000000000000000000
χ18222222222222-2-2-2-2-2-22200-2-200-222-200002000000000000000000
χ19222222222-2-2-22222-2-22-22200-2-2-2000002-20000000000000000000
χ20222222222-2-2-22222-2-22-2-2-20022-200000-220000000000000000000
χ21222222222-2-2-2-2-2-2-2222-200000020002-20002-20000000000000000
χ22222222222-2-2-2-2-2-2-2222-20000002000-22000-220000000000000000
χ2322222222-22-2-222-2-222-222200-2-2-200000-220000000000000000000
χ2422222222-22-2-222-2-222-22-2-20022-2000002-20000000000000000000
χ2522222222-22-2-2-2-222-2-2-2200000020002-2000-220000000000000000
χ2622222222-22-2-2-2-222-2-2-220000002000-220002-20000000000000000
χ2722222222-2-222-2-22222-2-2002200-222-20000-2000000000000000000
χ2822222222-2-222-2-22222-2-200-2-200-2-2-2200002000000000000000000
χ292222-2-2-2-2002-2002i−2i2i−2i00002-20002i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ302222-2-2-2-2002-2002i−2i2i−2i00002-20002i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ312222-2-2-2-2002-2002i−2i2i−2i0000-22000−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ322222-2-2-2-2002-2002i−2i2i−2i0000-22000−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ332222-2-2-2-2002-200−2i2i−2i2i00002-2000−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ342222-2-2-2-2002-200−2i2i−2i2i00002-2000−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ352222-2-2-2-2002-200−2i2i−2i2i0000-220002i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ362222-2-2-2-2002-200−2i2i−2i2i0000-220002i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ374444-4-4-4-400-44004i−4i−4i4i00000000000000000000000000000000000
χ384444-4-4-4-400-4400−4i4i4i−4i00000000000000000000000000000000000
χ3944-4-44-44-404000000000-4000000000000000002i−2i2i−2i000000000000
χ4044-4-44-44-404000000000-400000000000000000−2i2i−2i2i000000000000
χ4144-4-44-44-40-40000000004000000000000000002-2-22000000000000
χ4244-4-44-44-40-4000000000400000000000000000-222-2000000000000
χ434-44-4-444-44000000000-400000000000000000000002i−2i2i−2i00000000
χ444-44-4-444-44000000000-40000000000000000000000−2i2i−2i2i00000000
χ454-44-4-444-4-4000000000400000000000000000000002-2-2200000000
χ464-44-4-444-4-400000000040000000000000000000000-222-200000000
χ474-4-44-4-44400004-400000000004-4000000000000000000000000000
χ484-4-44-4-44400004-40000000000-44000000000000000000000000000
χ494-4-44-4-4440000-440000004-40000000000000000000000000000000
χ504-4-44-4-4440000-44000000-440000000000000000000000000000000
χ5188-8-8-88-88000000000000000000000000000000000000000000000
χ528-88-88-8-88000000000000000000000000000000000000000000000
χ538-8-8888-8-8000000000000000000000000000000000000000000000

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