C₃²⋊(C₁₃⋊C₃) #66852

order	351
isoclinism	isoclinic class of #66848
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃²

Aliases

unambiguous semidirect product	C₃²⋊(C₁₃⋊C₃)
unambiguous semidirect product	C₁₃⋊H(3,𝔽₃)
unambiguous semidirect product	(C₃×C₁₃⋊C₃)⋊C₃

Fitting	C₃²×C₁₃ ⋊ C₃
Sylow	C₁₃ ⋊ H(3,𝔽₃)

22 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:

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

Polycyclic presentation:

3^3,13|b^a=bc,d^a=d^3

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(351, 8);