GAP Manual: 54.2. Alpha

Alpha( G )

returns for a solvable group G a list whose i-th entry is the maximal derived length of groups G / ker(chi) for chiinIrr(G) with chi(1) at most the i-th irreducible degree of G.

The result is stored in the group record as G.alpha.

Note that calling this function will cause the computation of factor groups of G, so it works efficiently only for AG groups.

    gap> Alpha( Sl23 );
    [ 1, 3, 3 ]
    gap> Alpha( S4 );
    [ 1, 2, 3 ]