TITLE: Perfect group of order 190080
QUESTION [10 upvotes]: I need to know some properties of the perfect group of order $190080$
which is the Schur cover of the Mathieu group ${\rm M}_{12}$, but
when using PerfectGroup(190080), GAP runs so slowly.
Is there any other method in GAP for getting this group?

REPLY [12 votes]: Just write
gap> G := PerfectGroup(IsPermGroup,190080);
M12 2^1

in order to get the desired group as a permutation group:
gap> GeneratorsOfGroup(G);
[ (3,6)(7,10)(9,12)(13,16)(15,18)(19,22)(20,23)(21,24),
  (1,2,3)(4,5,7)(6,8,9)(10,11,13)(12,14,15)(16,17,19)(18,20,21)(22,24,23),
  (1,4)(2,5)(3,7)(6,10)(8,11)(9,13)(12,16)(14,17)(15,19)(18,22)(20,24)(21,23)
 ]

Now computations should be fast.
(If you omit the first argument, you get the group as a finitely presented group, and computations with such groups are inefficient for the obvious reasons.)