48.36 NrPolyhedralSubgroups

NrPolyhedralSubgroups( tbl, c1, c2, c3 )

returns the number and isomorphism type of polyhedral subgroups of the group with character table tbl which are generated by an element g of class c1 and an element h of class c2 with the property that the product gh lies in class c3.

    gap> NrPolyhedralSubgroups(L3_2, 2, 2, 4);
    rec(
      number := 21,
      type := "D8" ) 

According to~cite[p.~233]NPP84 the number of polyhedral subgroups of isomorphism type V_4, D_{2n}, A_4, S_4 and A_5 can be derived from the class multiplication coefficient (see ClassMultCoeffCharTable) and the number of Galois conjugates of a class (see ClassOrbitCharTable).

Note that the classes c1, c2 and c3 in the parameter list must be ordered according to the order of the elements in these classes.

Previous Up Top Next
Index

GAP 3.4.4
April 1997