C₄×Dic₇ #1137

order	112
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = #120×AGL(1,𝔽₇) (order 1344) · Inn(G) = D₇ · Out(G) = C₃×#120
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

direct product	C₄×Dic₇
unambiguous semidirect product	C₇⋊C₄²

C₇ ⋊ C₄²

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 2 generators on 15 points:

(2,3)(4,5)(6,7)(12,13,14,15);(1,2,4,6,7,5,3)(8,9,10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(112, 10);