In mathematics, especially in areas of abstract algebra and finite geometry, the list of transitive finite linear groups is an important classification of certain highly symmetric actions of finite groups on vector spaces.
The solvable finite 2-transitive groups were classified by Bertram Huppert.
[1] The classification of finite simple groups made possible the complete classification of finite doubly transitive permutation groups.
This article provides a complete list of the finite 2-transitive groups whose socle is elementary abelian.
There are four infinite classes of finite transitive linear groups.
Hence, it has a natural representation as a subgroup of the 7-dimensional orthogonal group O(7, q).
Factoring out with the radical, one obtains an isomorphism between O(7, q) and the symplectic group Sp(6, q).
The notation 21+4− stands for the extraspecial group of minus type of order 32 (i.e. the extraspecial group of order 32 with an odd number (namely one) of quaternion factor).
In the computer algebra programs GAP and MAGMA, these groups can be accessed with the command PrimitiveGroup(p^d,k); where the number k is the primitive identification of
Many books[3][4] and papers give a list of these groups, some of them an incomplete one.
For example, Cameron's book[5] misses the groups in line 11 of the table, that is, containing