C₃×C₁₁⋊#11759816 #45689586

order	33462
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃×C₁₃

Aliases

direct product	C₃×C₁₁⋊#11759816
unambiguous semidirect product	C₁₁⋊(C₃×#11759816)

Splittings

Fitting, socle	C₃×C₁₁×C₁₃² ⋊ C₂×C₃
derived, Hall	C₁₁×C₁₃² ⋊ C₂×C₃²
Hall	C₃×C₁₁×#92789 ⋊ C₂
Hall	C₁₁⋊(C₁₃⋊D₁₃) ⋊ C₃²
Hall	C₃×#92789 ⋊ D₁₁
Sylow	C₁₃² ⋊ C₃²×D₁₁
Sylow	C₁₁ ⋊ C₃×#11759816

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₁⋊#11759816
commutator, cosocle, hypocenter	C₁₁×C₁₃²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃²	C₂×C₃
LCS	G ▷ C₁₁×C₁₃²
UCS	C₁ ◁ C₃

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 1287

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33462, 94);

C3×C11⋊#11759816 #45689586