C₂²×Dic₇ #1162

order	112
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = AGL(1,𝔽₇)×#5934 (order 8064) · Inn(G) = D₇ · Out(G) = C₃×#5934
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×Dic₇

C₇ ⋊ C₂²×C₄

54 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(112, 35);