C₃²×C₄⋊Dic₅ #10623843

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

Aliases

direct product	C₃²×C₄⋊Dic₅
unambiguous semidirect product	C₄⋊(C₃²×Dic₅)

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

156 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 312);