C₁₁×C₃⋊(C₂₃⋊D₂₃) #46853568

order	34914
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₂₃

Aliases

direct product	C₁₁×C₃⋊(C₂₃⋊D₂₃)
unambiguous semidirect product	C₃⋊(C₁₁×C₂₃⋊D₂₃)

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₂₃² ⋊ C₂
derived, Hall	C₃×C₂₃² ⋊ C₂×C₁₁
Hall	C₁₁×C₂₃² ⋊ D₃
Sylow	C₂₃² ⋊ D₃×C₁₁
Hall	C₃×C₁₁ ⋊ C₂₃⋊D₂₃
Sylow	C₃ ⋊ C₁₁×C₂₃⋊D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	C₃⋊(C₂₃⋊D₂₃)
commutator, cosocle, hypocenter	C₃×C₂₃²	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₂₃²	C₂
LCS	G ▷ C₃×C₂₃²
UCS	C₁ ◁ C₁₁

208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 17457

A minimal faithful permutation representation — 3 generators on 60 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)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60);(12,13,14)(38,39,41,43,45,47,49,51,53,55,57,59,60,58,56,54,52,50,48,46,44,42,40);(15,16,18,20,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23,21,19,17)

Conjugacy classes & character table

8745 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34914, 84);

C11×C3⋊(C23⋊D23) #46853568