D₃×C₁₁×C₂₃ #13095010

order	1518
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₁×C₂₃
unambiguous semidirect product	C₃⋊(C₂×C₁₁×C₂₃)

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

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 759

A minimal faithful permutation representation — 2 generators on 37 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1518, 8);