C₉×#261 #90834

order	468
isoclinism	isoclinic class of #261
automorphism	Aut(G) = C₂×C₃×AGL(1,𝔽₁₃) (order 936) · Inn(G) = #261 · Out(G) = C₂×C₃²
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

Fitting, Hall	C₉×C₁₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄×C₉

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 117

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 9);