C₉×Dic₁₀ #67085

order	360
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂×C₃×D₄×AGL(1,𝔽₅) (order 960) · Inn(G) = C₂×D₅ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×Dic₁₀
unambiguous semidirect product	C₅⋊(Q₈×C₉)

Hall	C₅×C₉ ⋊ Q₈
Sylow	C₅ ⋊ Q₈×C₉

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 360

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 15);