C₁₁×C₃⋊D₃×C₂₃ #17986925

order	4554
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₁×C₃⋊D₃×C₂₃
unambiguous semidirect product	C₃⋊(D₃×C₁₁×C₂₃)

	subgroup	G/H
center, hypercenter	C₁₁×C₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₁×C₂₃

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 2277

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(15,16,17);(12,13,14)

1518 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 27);