C₃²×Dic₁₀ #67160

order	360
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×Dic₁₀
unambiguous semidirect product	C₅⋊(C₃²×Q₈)

Hall	C₃²×C₅ ⋊ Q₈
Sylow	C₅ ⋊ C₃²×Q₈

72 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)(7,8,9,10)(11,14,13,12)(15,16,17,18,19);(4,5,6)(7,11,9,13)(8,12,10,14)(16,19)(17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 90);