Automorphism group of the 8-dimensional cube graph

We illustrate the use of some of the automorphism group functions on the graph of the 8-dimensional cube.

> g := KCubeGraph(8);
> aut := AutomorphismGroup(g);
> Order(aut), FactoredOrder(aut);
10321920 [ <2, 15>, <3, 2>, <5, 1>, <7, 1> ]
> CompositionFactors(aut);
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Alternating(8)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
> IsVertexTransitive(g);
true
> IsEdgeTransitive(g);
true
> IsSymmetric(g);
true
> IsDistanceTransitive(g);
true
> IntersectionArray(g);
[ 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8 ]

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