Part of my group theory project involves we're looking at the group $U_4(3)$, which has abnormally large Schur Multiplier (36) and large automorphism group ($D_{12}$). I need to work with the central extensions by a group with order divisible by 3 in GAP: specifically, I would like the groups $$3.U_4(3), 6.U_4(3), 12.U_4(3).$$ I know that GAP has the command SchurCover(), but it returns a finitely presented group which takes too long to convert to a permutation group. Any calculations with group extensions and TwoCohomologyGeneric take very long. Also, the order of these groups exceeds 2 million, and thus are not in the perfect group library, so I am out of ideas.
Any thoughts would be appreciated!
In case someone is still interested, I have constructed the cover of $U_4(3)$, of order $36\cdot|U_4(3)|$, as a permutation group (and in the construction process have proven that it is unique, up to isomorphism).
This group can be found at https://github.com/hulpke/perfect/tree/main/particulars