C₂×#595 #3634

order	136
isoclinism	isoclinic class of #595
automorphism	Aut(G) = C₂×AGL(1,𝔽₁₇) (order 544) · Inn(G) = #595 · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×#595
unambiguous semidirect product	D₁₇⋊C₄

Fitting, socle	C₂×C₁₇ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₂×C₄

16 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(136, 13);