C₉×Dic₁₃ #90829

order	468
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂²×C₃×AGL(1,𝔽₁₃) (order 1872) · Inn(G) = D₁₃ · Out(G) = C₂³×C₃²
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×Dic₁₃

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

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 468

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4)(5,6,8,7,9,11,10,12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);(14,15,17,19,21,23,25,26,24,22,20,18,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 4);