C₂×C₇×Dic₇ #87646

order	392
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×Dic₇
unambiguous semidirect product	(C₂×C₇)⋊(C₄×C₇)

derived	C₇ ⋊ C₂×C₄×C₇
Sylow	C₇² ⋊ C₂×C₄

47 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 56

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2)(3,4,5,6)(8,9)(10,11)(12,13)(14,15,16,17,18,19,20);(1,2)(7,8,10,12,13,11,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 26);