Finite Group Databasebeta

← Group #98384

Character table — Group #98384

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444222244444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-11-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-111-11-11-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1111-1-111-11-11-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-111111-1-111-1-11-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-111111-1-111-1-11-1-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-111-1-11-1-1-1-1-111111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-11111-1-1-1-1-1-111-1-11-1-1-1-1-111111-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-111-11-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-111-11-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222-2-20022-200-2-2020-200000000000000000000
χ18222222222222-2-2-2-222-2-200-2-2-200220-20200000000000000000000
χ192222222222-2-222-2-2-2-2222200-2-2-20020-2000000000000000000000
χ202222222222-2-222-2-2-2-222-2-200-22200-202000000000000000000000
χ212222222222-2-2-2-222-2-2-2-200002000000002-22-20000000000000000
χ222222222222-2-2-2-222-2-2-2-20000200000000-22-220000000000000000
χ2322222222-2-222-2-222-2-2220022-200-2-20-20200000000000000000000
χ2422222222-2-222-2-222-2-22200-2-2-20022020-200000000000000000000
χ2522222222-2-2-2-2222222-2-22200-22200-20-2000000000000000000000
χ2622222222-2-2-2-2222222-2-2-2-200-2-2-200202000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2222200002000000002-2-220000000000000000
χ2822222222-2-2-2-2-2-2-2-222220000200000000-222-20000000000000000
χ2922-22-2-2-2200002-22i−2i2i−2i002-20002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ3022-22-2-2-2200002-22i−2i2i−2i002-20002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ3122-22-2-2-2200002-22i−2i2i−2i00-22000−2i2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ3222-22-2-2-2200002-22i−2i2i−2i00-22000−2i2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ3322-22-2-2-2200002-2−2i2i−2i2i002-2000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ3422-22-2-2-2200002-2−2i2i−2i2i002-2000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ3522-22-2-2-2200002-2−2i2i−2i2i00-220002i−2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ3622-22-2-2-2200002-2−2i2i−2i2i00-220002i−2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ3744-44-4-4-440000-444i−4i−4i4i00000000000000000000000000000000000
χ3844-44-4-4-440000-44−4i4i4i−4i00000000000000000000000000000000000
χ3944-4-444-4-400000000004i−4i00000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4044-4-444-4-400000000004i−4i0000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4144-4-444-4-40000000000−4i4i00000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4244-4-444-4-40000000000−4i4i0000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ434-4444-4-4-44-40000000000000000000000000000000000000002-22-2
χ444-4444-4-4-44-4000000000000000000000000000000000000000-22-22
χ454-4444-4-4-4-440000000000000000000000000000000000000002i−2i−2i2i
χ464-4444-4-4-4-44000000000000000000000000000000000000000−2i2i2i−2i
χ474-4-4-44-444004-40000000000000004-4000000000000000000000000
χ484-4-4-44-444004-4000000000000000-44000000000000000000000000
χ494-4-4-44-44400-4400000000004-400000000000000000000000000000
χ504-4-4-44-44400-440000000000-4400000000000000000000000000000
χ51888-8-8-88-8000000000000000000000000000000000000000000000
χ528-88-8-88-88000000000000000000000000000000000000000000000
χ538-8-88-888-8000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.