C₁₁×D₉×C₁₉ #16836769

order	3762
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₉×C₁₉
unambiguous semidirect product	C₉⋊(C₂×C₁₁×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₁×C₁₉
Frattini	C₃	D₃×C₁₁×C₁₉
Fitting	C₉×C₁₁×C₁₉	C₂
socle	C₃×C₁₁×C₁₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₁×C₁₉

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1881

A minimal faithful permutation representation — 2 generators on 39 points:

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

1254 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3762, 9);