order	224
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = C₂⁶×AGL(1,𝔽₇) (order 2688) · Inn(G) = C₂×D₇ · Out(G) = C₂⁵×C₃
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

Fitting	C₂²×C₄×C₇ ⋊ C₂
Sylow	C₇ ⋊ C₄×D₄

94 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 123);