Since groups are domains, the recommended command to compute the order of a group is Size (30.4-6). For convenience, group orders can also be computed ...
The 1st element of the returned list in this example is Group( () )^G - the conjugacy class of the trivial subgroup, but in general the order in which the classes are ...
Let order be of the form p^{2n+1}, for a prime integer p and a positive integer n. ExtraspecialGroup returns the extraspecial group of order order that is ...
This permutation group has order 2592, and 54 Conjugacy Classes. I can obtain a class representative for each with Conjug ...
Primitive groups of equal degree and size are in no particular order. gap> g := PrimitiveGroup( 8, 1 ); AGL(1,8) gap> g.generators; [ (1,2,3,4,5,6,7), (1,8)(2,4)(3 ...
We give the first order-optimal algorithm for the $k$-secretary problem under
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gap> G:=SmallGroup(8,1); # Set G to be a group of order 8.
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In this section, we wish to discover some non-trivial groups with an interesting property: namely, that the average order of their elements is an integer. The GAP ...