Finite Group Databasebeta

← Group #98317

Character table — Group #98317

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11-1-11-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-11-1-11-11-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1-1-111111-11-11-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-111-1-1111111-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-111-1-1111111-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-111-1-1-1-11-1-111-11-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-11111-1-1-1-1-1-111-1-1-1-11-1-111-11-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222-2-2000022-2-2-20-20200000000000000000000
χ18222222222222-2-2-2-222-2-20000-2-2-222020-200000000000000000000
χ192222222222-2-2222-2-2-22-2222200-200-20-2000000000000000000000
χ202222222222-2-2222-2-2-22-2-2-2-2-200-200202000000000000000000000
χ212222222222-2-2-2-2-22-2-2-2200000020000002-22-20000000000000000
χ222222222222-2-2-2-2-22-2-2-220000002000000-22-220000000000000000
χ2322222222-2-222-2-222-2-222000022-2-2-2020-200000000000000000000
χ2422222222-2-222-2-222-2-2220000-2-2-2220-20200000000000000000000
χ2522222222-2-2-2-222-2222-2222-2-200-200-202000000000000000000000
χ2622222222-2-2-2-222-2222-22-2-22200-20020-2000000000000000000000
χ2722222222-2-2-2-2-2-22-2222-200000020000002-2-220000000000000000
χ2822222222-2-2-2-2-2-22-2222-20000002000000-222-20000000000000000
χ29222-22-2-2-22-2002-22000-202-22-2000000000000000002−22−200002−22−2
χ30222-22-2-2-22-2002-22000-202-22-200000000000000000−22−220000−22−22
χ31222-22-2-2-22-2002-22000-20-22-22000000000000000002−22−20000−22−22
χ32222-22-2-2-22-2002-22000-20-22-2200000000000000000−22−2200002−22−2
χ33222-22-2-2-2-22002-2-2000202-2-2200000000000000000i2−i2−i2i20000i2−i2−i2i2
χ34222-22-2-2-2-22002-2-2000202-2-2200000000000000000−i2i2i2−i20000−i2i2i2−i2
χ35222-22-2-2-2-22002-2-200020-222-200000000000000000i2−i2−i2i20000−i2i2i2−i2
χ36222-22-2-2-2-22002-2-200020-222-200000000000000000−i2i2i2−i20000i2−i2−i2i2
χ37444-44-4-4-44-400-44-400040000000000000000000000000000000000
χ38444-44-4-4-4-4400-444000-40000000000000000000000000000000000
χ3944-4-4-444-4000000004i−4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4044-4-4-444-4000000004i−4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4144-4-4-444-400000000−4i4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4244-4-4-444-400000000−4i4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ434-44-4-4-44400000004000-4000000000000000002i−2i2i−2i000000000000
χ444-44-4-4-44400000004000-400000000000000000−2i2i−2i2i000000000000
χ454-44-4-4-4440000000-40004000000000000000002-2-22000000000000
χ464-44-4-4-4440000000-4000400000000000000000-222-2000000000000
χ474-4-444-44-4004-40000000000000004i−4i000000000000000000000000
χ484-4-444-44-4004-4000000000000000−4i4i000000000000000000000000
χ494-4-444-44-400-440000000000004i−4i000000000000000000000000000
χ504-4-444-44-400-44000000000000−4i4i000000000000000000000000000
χ5188-88-8-8-88000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-8-8-888-88000000000000000000000000000000000000000000000

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