order	224
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = C₂²×#120×AGL(1,𝔽₇) (order 5376) · Inn(G) = C₂×D₇ · Out(G) = C₂³×C₃×D₄
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Dic₁₄

Splittings

C₇ ⋊ C₄×Q₈

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 63);