C₂×#1157 #6545

order	224
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = AGL(1,𝔽₇)×#23900 (order 10752) · Inn(G) = C₂×D₇ · Out(G) = C₃×#2403
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₂²×C₄×C₇ ⋊ C₂
Sylow	C₇ ⋊ C₂×#41

164 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 177);