D₉×C₂₅ #90636

order	450
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₄×C₅×AGL(1,ℤ/9) (order 1080) · Inn(G) = D₉ · Out(G) = C₃×C₄×C₅
homology	Abelianization (H₁) = C₂×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₉×C₂₅
unambiguous semidirect product	C₉⋊(C₂×C₂₅)

Fitting, Hall	C₉×C₂₅ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₂₅

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 225

A minimal faithful permutation representation — 2 generators on 34 points:

(2,4)(3,7)(5,8)(6,9)(10,11,13,16,20,12,14,17,21,25,15,18,22,26,29,19,23,27,30,32,24,28,31,33,34);(1,6,4,3,8,5,7,2,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 1);