C₂×#3624 #63246

order	272
isoclinism	isoclinic class of #595
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₇) (order 2176) · Inn(G) = #595 · Out(G) = C₄×D₄
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₁₇ ⋊ C₂×C₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 2 generators on 27 points:

(3,4,5,7,6,8,9,10)(12,13,14,16)(15,18,19,23)(17,22,20,21)(24,26,27,25);(1,2)(11,12,15,20,16,21,25,27,23,18,24,26,22,13,17,19,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 33);