C₂×#3633 #63264

order	272
isoclinism	isoclinic class of #3633
automorphism	Aut(G) = C₂×AGL(1,𝔽₁₇) (order 544) · Inn(G) = #3633 · Out(G) = C₂²
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

Fitting, socle	C₂×C₁₇ ⋊ C₈
derived, Sylow	C₁₇ ⋊ C₂×C₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 34

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 51);