C₅×C₃⋊(C₃⋊#157) #13108532

order	1620
isoclinism	isoclinic class of C₃⋊(C₃⋊#157)
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₅×C₃⋊(C₃⋊#157)
unambiguous semidirect product	C₃⋊(C₅×C₃⋊#157)

Fitting, socle, Hall	C₃⁴×C₅ ⋊ C₄
derived, Sylow	C₃⁴ ⋊ C₄×C₅

208 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 438);