Isoclinic Groups

Two Groups $G$ and $H$ are said to be isoclinic if there are isomorphisms $G/Z(G)\to H/Z(H)$ and $G'\to H'$, where $Z(G)$ is the Center of the group, which identify the two commutator maps.

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. ``Isoclinism.'' §6.7 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, pp. xxiii-xxiv, 1985.