If n is greater than 4,then the nth one of these groups is simple.
The Schur multipliers of the fourth and  fth of these groups, as well as theeighth and beyond, are the cyclic groups of order two, while the Schur multipliersof the sixth and seventh are the cyclic groups of order six. These groups areassociated with graphs named for them, and the fourth of those graphs is thecuboctahedral graph. The icosahedral group is equal to the direct product ofthe  fth of these groups and the second cyclic group. If n is greater than 4,then the nth one of these groups is simple. The group order of the nth of thesegroups is   n! . For ten points, identify these groups of all even permutations 2of a certain size
The Schur multipliers of the fourth and  fth of these groups, as well as theeighth and beyond, are the cyclic groups of order two, while the Schur multipliersof the sixth and seventh are the cyclic groups of order six.
alternating groups