C₃×C₁₁⋊(C₁₉⋊D₁₉) #37558548

order	23826
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₉

Aliases

direct product	C₃×C₁₁⋊(C₁₉⋊D₁₉)
unambiguous semidirect product	C₁₁⋊(C₃×C₁₉⋊D₁₉)

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₁₉² ⋊ C₂
derived, Hall	C₁₁×C₁₉² ⋊ C₂×C₃
Hall	C₃×C₁₉² ⋊ D₁₁
Sylow	C₁₉² ⋊ C₃×D₁₁
Hall	C₃×C₁₁ ⋊ C₁₉⋊D₁₉
Sylow	C₁₁ ⋊ C₃×C₁₉⋊D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₁⋊(C₁₉⋊D₁₉)
commutator, cosocle, hypocenter	C₁₁×C₁₉²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₉²	C₂
LCS	G ▷ C₁₁×C₁₉²
UCS	C₁ ◁ C₃

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 11913

A minimal faithful permutation representation — 3 generators on 52 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52);(4,5,7,9,11,13,14,12,10,8,6)(34,35,37,39,41,43,45,47,49,51,52,50,48,46,44,42,40,38,36);(15,16,18,20,22,24,26,28,30,32,33,31,29,27,25,23,21,19,17)

Conjugacy classes & character table

5961 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23826, 40);

C3×C11⋊(C19⋊D19) #37558548