Classification of groups of order 56

This article gives specific information, namely, classification, about a family of groups, namely: groups of order 56.
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The list

The following are the 13 groups of order 56:

Group	Second part of GAP ID	Abelian	Nilpotent	Direct Product
Nontrivial semidirect product of Z7 and Z8	1	no	no	no
Cyclic group:Z56	2	yes	yes	no
Dicyclic group:Dic56	3	no	no	no
Direct product of Z4 and D14	4	no	no	yes
Dihedral group:D56	5	no	no	no
Direct product of Z2 and Dic28	6	no	no	yes
Nontrivial semidirect product of Z7 and D8	7	no	no	no
Direct product of Z2 and Z28	8	yes	yes	yes
Direct product of Z7 and D8	9	no	yes	yes
Direct product of Z7 and Q8	10	no	yes	yes
General affine group:GA(1,8)	11	no	no	no
Direct product of V4 and D14	12	no	no	yes
Direct product of V4 and Z14	13	yes	yes	yes

The classification

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See also

• Classification of groups of order eight times a prime congruent to 7 modulo 8