C₃²×C₂²⋊Dic₅ #10623849

order	720
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂²×C₃

Aliases

Hall	C₃²×C₅ ⋊ C₂²⋊C₄
Sylow	C₅ ⋊ C₃²×C₂²⋊C₄

204 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 360

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 318);