Groups of order 7.2^n

This article discusses the groups of order $7\cdot 2^{n}$, where $n$ varies over nonnegative integers. Note that any such group has a 7-Sylow subgroup which is cyclic group:Z7, and a 2-Sylow subgroup, which is of order $2^{n}$. Further, because order has only two prime factors implies solvable, any such group is a solvable group.

Number of groups of small orders

Exponent $n$	Value $2^{n}$	Value $3\cdot 2^{n}$	Number of groups of order $7\cdot 2^{n}$	Reason/explanation/list
0	1	7	1	only cyclic group:Z7, see equivalence of definitions of group of prime order
1	2	14	2	See groups of order 14, classification of groups of order a product of two distinct primes
2	4	28	4	See groups of order 28
3	8	56	13	See groups of order 56
4	16	112	43	See groups of order 112
5	32	224	197	See groups of order 224
6	64	448	1396	See groups of order 448
7	128	896	19349	See groups of order 896
8	256	1792	1083553	See groups of order 1792