[GAP Forum] Filter 3-generator groups in GAP.

[Joy F.]

DearForum,
 
I wonder how do I build the following groups in GAP

  
1) Ordem G is 64, is 3-generator, then exist exactly four 2$\varepsilon$-group G such that exp(G/G') = exp(G')=2 satisfying G^2=G'.

2) Order G is 64, is 3-generator E-group, it can be checked in GAP that there exist no 2$\varepsilon$-group of order 64 having an abelian automorphism group.

Def. 2$\varepsilon$-group
G is 2$\varepsilon$-groups if G is 2$\varepsilon$-Engel group and exists a non-negative integer r such that Omega(G,2,r) < Z(G) and exp(G/G')=2^r.

How do I filter these groups in GAP?

JOY.