C₃×C₁₃×AGL(1,𝔽₁₁) #16864256

order	4290
isoclinism	isoclinic class of AGL(1,𝔽₁₁)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₃×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₃×C₅×C₁₃)
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₂×C₃×C₁₃)
unambiguous semidirect product	(C₃×D₁₁)⋊(C₅×C₁₃)
unambiguous semidirect product	(C₃×C₁₃×D₁₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₃×C₁₃	AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃	C₂×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₁₃

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 429

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(18,22,23,21,26,19,20,27,24,25);(17,18,21,26,20,23,27,22,25,24,19)

429 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 21);