order	234
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂×C₃×AGL(1,𝔽₁₃) (order 936) · Inn(G) = D₁₃ · Out(G) = C₂²×C₃²
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₃

Splittings

Fitting, Hall	C₉×C₁₃ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₉

12 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)(13,14)(15,16)(17,18)(19,20)(21,22);(10,11,13,15,17,19,21,22,20,18,16,14,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(234, 4);