C₉×C₂²⋊D₅ #67089

order	360
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂³×C₃×AGL(1,𝔽₅) (order 480) · Inn(G) = C₂×D₅ · Out(G) = C₂×C₃×C₄
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 19);