Finite Group Databasebeta

← Group #98367

Character table — Group #98367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444224444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1111-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-111-1-11111-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-111-1-11111-11-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-11-1-1-1-1-111-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-11-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-11111-1-1111-11-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-11111-1-1111-11-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-111-1-1-1-11-1-111111-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-11111-1-1-1-1-1-111-1-1-1-11-1-111111-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11-11-1-1111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11-11-1-1111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-222-2-2-2-22200-2-2-2000-20002000000000000000000
χ18222222222222-2-222-2-2-2-2-2-20022-20002000-2000000000000000000
χ192222222222-2-222-2-222-2-2002200-2-2-2-202000000000000000000000
χ202222222222-2-222-2-222-2-200-2-200-22220-2000000000000000000000
χ212222222222-2-2-2-2-2-2-2-2220000002000002-202-20000000000000000
χ222222222222-2-2-2-2-2-2-2-222000000200000-220-220000000000000000
χ2322222222-2-222-2-2-2-22222220022-2000-2000-2000000000000000000
χ2422222222-2-222-2-2-2-22222-2-200-2-2-200020002000000000000000000
χ2522222222-2-2-2-22222-2-222002200-2-2-220-2000000000000000000000
χ2622222222-2-2-2-22222-2-22200-2-200-222-202000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-20000002000002-20-220000000000000000
χ2822222222-2-2-2-2-2-22222-2-2000000200000-2202-20000000000000000
χ29222-2-2-2-22002-200002i−2i2i−2i2-2002i−2i000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ30222-2-2-2-22002-200002i−2i2i−2i2-2002i−2i00000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ31222-2-2-2-22002-200002i−2i2i−2i-2200−2i2i000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ32222-2-2-2-22002-200002i−2i2i−2i-2200−2i2i00000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ33222-2-2-2-22002-20000−2i2i−2i2i2-200−2i2i000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ34222-2-2-2-22002-20000−2i2i−2i2i2-200−2i2i00000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ35222-2-2-2-22002-20000−2i2i−2i2i-22002i−2i000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ36222-2-2-2-22002-20000−2i2i−2i2i-22002i−2i00000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ37444-4-4-4-4400-4400004i−4i−4i4i000000000000000000000000000000000
χ38444-4-4-4-4400-440000−4i4i4i−4i000000000000000000000000000000000
χ3944-4-44-44-400004-400000000000004i−4i000000000000000000000000
χ4044-4-44-44-400004-40000000000000−4i4i000000000000000000000000
χ4144-4-44-44-40000-44000000004i−4i00000000000000000000000000000
χ4244-4-44-44-40000-4400000000−4i4i00000000000000000000000000000
χ434-44-4-444-40000004i−4i000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ444-44-4-444-40000004i−4i00000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ454-44-4-444-4000000−4i4i000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ464-44-4-444-4000000−4i4i00000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ474-4-44-4-4444-40000000000000000000000000000000000000002i−2i2i−2i
χ484-4-44-4-4444-4000000000000000000000000000000000000000−2i2i−2i2i
χ494-4-44-4-444-440000000000000000000000000000000000000002-2-22
χ504-4-44-4-444-44000000000000000000000000000000000000000-222-2
χ5188-88-88-8-8000000000000000000000000000000000000000000000
χ528-8888-8-8-8000000000000000000000000000000000000000000000
χ538-8-8-888-88000000000000000000000000000000000000000000000

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