Finite Group Databasebeta

← Group #98412

Character table — Group #98412

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-11-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
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
χ911111111-1-11111-1-1-1-1-1-11111111-1-111-1-11-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-11111111-1-111-1-11-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-111111-1-111-1-1-1-1-1111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-11111-1-1-1-1-1-111111-1-111-1-1-1-1-1111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-111ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-111−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1111111-11-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1111111-11-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-222-2-2-2-22200-20022220000-2-2000000000000000000
χ182222222222-2-222-2-2-2-22200-200-2-2-2-2000022000000000000000000
χ19222222222-222-2-222-2-22-222-2-2-20000002-200000000000000000000
χ20222222222-222-2-222-2-22-2-2-2-222000000-2200000000000000000000
χ21222222222-2-2-2-2-2-2-2222-20020000002-200002-20000000000000000
χ22222222222-2-2-2-2-2-2-2222-2002000000-220000-220000000000000000
χ2322222222-2222-2-2-2-222-2222-2-2-2000000-2200000000000000000000
χ2422222222-2222-2-2-2-222-22-2-2-2220000002-200000000000000000000
χ2522222222-22-2-2-2-222-2-2-220020000002-20000-220000000000000000
χ2622222222-22-2-2-2-222-2-2-22002000000-2200002-20000000000000000
χ2722222222-2-2-2-2222222-2-200-20022-2-20000-22000000000000000000
χ2822222222-2-2-2-2222222-2-200-200-2-22200002-2000000000000000000
χ29222-2-2-2-222-2002-20000-22000002i−2i2i−2i000000002−22−2i2−i2i2−i200000000
χ30222-2-2-2-222-2002-20000-22000002i−2i2i−2i00000000−22−22−i2i2−i2i200000000
χ31222-2-2-2-222-2002-20000-2200000−2i2i−2i2i000000002−22−2−i2i2−i2i200000000
χ32222-2-2-2-222-2002-20000-2200000−2i2i−2i2i00000000−22−22i2−i2i2−i200000000
χ33222-2-2-2-22-22002-200002-2000002i−2i−2i2i00000000i2−i2−i2i2−222−200000000
χ34222-2-2-2-22-22002-200002-2000002i−2i−2i2i00000000−i2i2i2−i22−2−2200000000
χ35222-2-2-2-22-22002-200002-200000−2i2i2i−2i00000000i2−i2−i2i22−2−2200000000
χ36222-2-2-2-22-22002-200002-200000−2i2i2i−2i00000000−i2i2i2−i2−222−200000000
χ37444-4-4-4-444400-440000-4-4000000000000000000000000000000000
χ38444-4-4-4-44-4-400-44000044000000000000000000000000000000000
χ3944-44-4-44-40000004i−4i0000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4044-44-4-44-40000004i−4i000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ4144-44-4-44-4000000−4i4i0000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ4244-44-4-44-4000000−4i4i000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ434-44-44-44-4000000004i−4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ444-44-44-44-4000000004i−4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ454-44-44-44-400000000−4i4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ464-44-44-44-400000000−4i4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ474-4-4-4-4444004-4000000000004-40000000000000000000000000000
χ484-4-4-4-4444004-400000000000-440000000000000000000000000000
χ494-4-4-4-444400-44000000004-40000000000000000000000000000000
χ504-4-4-4-444400-4400000000-440000000000000000000000000000000
χ5188-8-888-8-8000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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