An infinite family of finite 2-groups with fixed co-class

In [1] six pro-2-groups of finite and fixed coclasses is studied. Infinite sequences of finite 2-groups arising from this pro2-groups also investigated. One of the five infinite sequences associated with the pro-2-group S = ha, u | a 2 = u 4 ,(u 2 ) a = u minus;2 i is the sequence Gj (1, 2) = ha, u | a 2 u minus;4 (u minus;1 a) 2 j ,(u 2 ) a u 2 (u minus;1 a) 2 j+1 ,(u minus;1 a) 2 j+2 i. In this paper we calculate the orders of the members of this infinite family.