C₃²×C₁₃⋊C₃ #66857

order	351
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₃²×C₁₃⋊C₃
unambiguous semidirect product	C₁₃⋊C₃³
unambiguous semidirect product	(C₃×C₁₃)⋊C₃²

Fitting, socle	C₃²×C₁₃ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃³

	subgroup	G/H
center, hypercenter	C₃²	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃³
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃²

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 117

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(351, 13);