Finite Group Databasebeta

← Group #98358

Character table — Group #98358

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444444222244444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-11-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-11-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-111-11-1-1-11-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1111-1-111-11-1-1-11-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-111111-1-111-1-1-1-11-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-111111-1-111-1-1-1-11-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-222-2-2-2-222-200-2-2002000-20000000000000000000
χ18222222222222-2-222-2-2-2-2-2-2-2002200-200020000000000000000000
χ192222222222-2-222-2-2-2-22200-22200-2-202000-2000000000000000000
χ202222222222-2-222-2-2-2-22200-2-2-200220-20002000000000000000000
χ212222222222-2-2-2-2-2-222-2-2002000000002-2002-20000000000000000
χ222222222222-2-2-2-2-2-222-2-200200000000-2200-220000000000000000
χ2322222222-2-222-2-2-2-2222222-2002200-2000-20000000000000000000
χ2422222222-2-222-2-2-2-22222-2-2-200-2-200200020000000000000000000
χ2522222222-2-2-2-2222222-2-200-22200-2-20-20002000000000000000000
χ2622222222-2-2-2-2222222-2-200-2-2-2002202000-2000000000000000000
χ2722222222-2-2-2-2-2-222-2-222002000000002-200-220000000000000000
χ2822222222-2-2-2-2-2-222-2-22200200000000-22002-20000000000000000
χ29222-22-2-2-2002-200002i−2i2i−2i2-20002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ30222-22-2-2-2002-200002i−2i2i−2i2-20002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ31222-22-2-2-2002-200002i−2i2i−2i-22000−2i2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ32222-22-2-2-2002-200002i−2i2i−2i-22000−2i2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ33222-22-2-2-2002-20000−2i2i−2i2i2-2000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ34222-22-2-2-2002-20000−2i2i−2i2i2-2000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ35222-22-2-2-2002-20000−2i2i−2i2i-220002i−2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ36222-22-2-2-2002-20000−2i2i−2i2i-220002i−2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ37444-44-4-4-400-4400004i−4i−4i4i000000000000000000000000000000000
χ38444-44-4-4-400-440000−4i4i4i−4i000000000000000000000000000000000
χ3944-44-44-4-40000004i−4i000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4044-44-44-4-40000004i−4i00000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4144-44-44-4-4000000−4i4i000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4244-44-44-4-4000000−4i4i00000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ434-44-4-444-44-40000000000000000000000000000000000000002i−2i2i−2i
χ444-44-4-444-44-4000000000000000000000000000000000000000−2i2i−2i2i
χ454-44-4-444-4-440000000000000000000000000000000000000002-2-22
χ464-44-4-444-4-44000000000000000000000000000000000000000-222-2
χ474-4-4-444-4400004-400000000000004-4000000000000000000000000
χ484-4-4-444-4400004-40000000000000-44000000000000000000000000
χ494-4-4-444-440000-440000000004-40000000000000000000000000000
χ504-4-4-444-440000-44000000000-440000000000000000000000000000
χ5188-8-8-8-888000000000000000000000000000000000000000000000
χ528-888-8-8-88000000000000000000000000000000000000000000000
χ538-8-888-88-8000000000000000000000000000000000000000000000

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