C₅×C₃⋊(C₃⋊C₁₆) #10623623

order	720
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₆ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₃⋊(C₃⋊C₁₆)
unambiguous semidirect product	C₃⋊(C₅×C₃⋊C₁₆)

derived, Sylow	C₃² ⋊ C₅×C₁₆
Hall	C₃²×C₅ ⋊ C₁₆

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 3 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 92);