order	224
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = C₂²×C₄×AGL(1,𝔽₇) (order 672) · Inn(G) = D₇ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

D₇×C₁₆

Splittings

Fitting	C₇×C₁₆ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₁₆

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 2 generators on 23 points:

(2,3)(4,5)(6,7);(1,2,4,6,7,5,3)(8,9,10,13,11,14,16,19,12,15,17,20,18,21,22,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 3);