order	224
automorphism	Aut(G) = C₂²×D₄×AGL(1,𝔽₇) (order 1344) · Inn(G) = C₂²×D₇ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

D₇×M₁₆

Splittings

Fitting	C₇×M₁₆ ⋊ C₂
Sylow	C₇ ⋊ C₂×M₁₆

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 56

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 101);