non abelian

Question

1. Let G be a non abelian group, order of G can be
   1.   24
   2.   44
   3.   54
   4.   34

Answer 1

break all the number in there prime factor and refer this https://math.stackexchange.com/questions/1126354/order-of-non-abelian-group-cant-be-what

24 will be the answer & every group of order p^2 is abelian so 44 will be discarded and  for rest option refer the link  

Comments

what value of p gives  p² =44?

and the explanation there i have quoted here

Suppose p divides q−1 then there is a unique nonabelian group of order pq,obviously upto isomorphism.

option 2 => 54

can be written as 2 * 3³

p =27 and q-1 = 2-1 =1

27 divides 1 so 54 can be order of non abelian right