# Factor group

Let N be a normal subgroup of a group G. The **factor group** or ** quotient group** G/N is the set of all left cosets of N in G, i.e.:

For each aN and bN in G/N, the

- (aN)(bN) = a(Nb)N = a(bN)N = (ab)NN = (ab)N.

The inverse of an element aN of G/N is a^{-1}N.

### Example

The factor group G/T of a space group G and its translation

### See also

Chapter 8 in the *International Tables of Crystallography, Volume A*