C₃×#595 #6076

order	204
isoclinism	isoclinic class of #595
automorphism	Aut(G) = C₂×AGL(1,𝔽₁₇) (order 544) · Inn(G) = #595 · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle, Hall	C₃×C₁₇ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₃×C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 51

A minimal faithful permutation representation — 2 generators on 20 points:

(2,6,4,3)(5,13,9,8)(7,11,10,12)(14,15,17,16)(18,19,20);(1,2,5,10,6,11,15,17,13,8,14,16,12,3,7,9,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(204, 5);