order	224
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = AGL(1,𝔽₇)×#15947 (order 10752) · Inn(G) = C₂×D₇ · Out(G) = C₃×#2403
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

Splittings

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

132 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 122);