D₄×D₇ #1158

order	112
automorphism	Aut(G) = C₂×D₄×AGL(1,𝔽₇) (order 672) · Inn(G) = C₂²×D₇ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₄×D₇

Fitting	C₇×D₄ ⋊ C₂
Sylow	C₇ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 28

A minimal faithful permutation representation — 3 generators on 11 points:

(2,3)(4,5)(6,7);(1,2,4,6,7,5,3)(9,11);(8,9)(10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(112, 31);