C₉×#168 #67072

order	360
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂³×C₃×AGL(1,𝔽₅) (order 480) · Inn(G) = D₅ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₈×C₉ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₅ ⋊ C₈×C₉
Hall	C₅×C₉ ⋊ C₈

24 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 2);