C₉×D₂₀ #67087

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) = C₂

Aliases

direct product	C₉×D₂₀
unambiguous semidirect product	C₄⋊(C₉×D₅)

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 17);