C₅×C₄⋊(C₃⋊Dic₃) #10623891

order	720
isoclinism	isoclinic class of #634
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₅×C₄⋊(C₃⋊Dic₃)
unambiguous semidirect product	C₄⋊(C₅×C₃⋊Dic₃)

Hall	C₃²×C₅ ⋊ C₄⋊C₄
Sylow	C₃² ⋊ C₅×C₄⋊C₄

156 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 360);