Finite Group Databasebeta

← Group #98355

Character table — Group #98355

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-11-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-11-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-1111-1-1111111-1-1-11-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-11111-1-1-1-1-1-1111-1-1111111-1-1-11-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-222-2-2-2-222-200-2-20000-2200000000000000000000
χ18222222222222-2-222-2-2-2-2-2-2-2002200002-200000000000000000000
χ192222222222-2-222-2-222-2-200-22200-2-20000-22000000000000000000
χ202222222222-2-222-2-222-2-200-2-2-2002200002-2000000000000000000
χ212222222222-2-2-2-2-2-2-2-2220020000002-200002-20000000000000000
χ222222222222-2-2-2-2-2-2-2-222002000000-220000-220000000000000000
χ2322222222-2-222-2-2-2-2222222-200-2-200002-200000000000000000000
χ2422222222-2-222-2-2-2-22222-2-2-200220000-2200000000000000000000
χ2522222222-2-2-2-22222-2-22200-22200220000-2-2000000000000000000
χ2622222222-2-2-2-22222-2-22200-2-2-200-2-2000022000000000000000000
χ2722222222-2-2-2-2-2-22222-2-20020000002-20000-220000000000000000
χ2822222222-2-2-2-2-2-22222-2-2002000000-2200002-20000000000000000
χ2922-2-222-2-200002-22i−2i002i−2i0002-2002i−2i000000001+i−1−i1−i−1+i00001+i−1−i1−i−1+i0000
χ3022-2-222-2-200002-22i−2i002i−2i0002-2002i−2i00000000−1−i1+i−1+i1−i0000−1−i1+i−1+i1−i0000
χ3122-2-222-2-200002-22i−2i002i−2i000-2200−2i2i000000001+i−1−i1−i−1+i0000−1−i1+i−1+i1−i0000
χ3222-2-222-2-200002-22i−2i002i−2i000-2200−2i2i00000000−1−i1+i−1+i1−i00001+i−1−i1−i−1+i0000
χ3322-2-222-2-200002-2−2i2i00−2i2i0002-200−2i2i000000001−i−1+i1+i−1−i00001−i−1+i1+i−1−i0000
χ3422-2-222-2-200002-2−2i2i00−2i2i0002-200−2i2i00000000−1+i1−i−1−i1+i0000−1+i1−i−1−i1+i0000
χ3522-2-222-2-200002-2−2i2i00−2i2i000-22002i−2i000000001−i−1+i1+i−1−i0000−1+i1−i−1−i1+i0000
χ3622-2-222-2-200002-2−2i2i00−2i2i000-22002i−2i00000000−1+i1−i−1−i1+i00001−i−1+i1+i−1−i0000
χ3744-4-444-4-40000-444i−4i00−4i4i000000000000000000000000000000000
χ3844-4-444-4-40000-44−4i4i004i−4i000000000000000000000000000000000
χ3944-4-4-4-4444-40000000000000000000000000000000000000002i−2i2i−2i
χ4044-4-4-4-4444-4000000000000000000000000000000000000000−2i2i−2i2i
χ4144-4-4-4-444-440000000000000000000000000000000000000002-2-22
χ4244-4-4-4-444-44000000000000000000000000000000000000000-222-2
χ434-44-44-44-4000000004i−4i000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ444-44-44-44-4000000004i−4i00000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ454-44-44-44-400000000−4i4i000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ464-44-44-44-400000000−4i4i00000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ474-4-44-444-4004-400000000000004i−4i00000000000000000000000000
χ484-4-44-444-4004-40000000000000−4i4i00000000000000000000000000
χ494-4-44-444-400-44000000004i−4i0000000000000000000000000000000
χ504-4-44-444-400-4400000000−4i4i0000000000000000000000000000000
χ518888-8-8-8-8000000000000000000000000000000000000000000000
χ528-88-8-88-88000000000000000000000000000000000000000000000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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