C₁₁×#4208 #13184161

order	1782
isoclinism	isoclinic class of #272
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×#4208

Splittings

Fitting, Hall	C₁₁×#737 ⋊ C₂
Sylow	#737 ⋊ C₂×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₁	C₃⋊D₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂×C₃×C₁₁
Frattini	C₃	C₃×C₁₁×C₃⋊D₃
Fitting	C₁₁×#737	C₂
socle	C₃×C₁₁	C₃×C₃⋊D₃
prime radical	C₁₁×#272	C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₉×C₁₁

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 297

A minimal faithful permutation representation — 3 generators on 38 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1782, 85);

C11×#4208 #13184161