C₁₁×C₂₃×#261 #27190448

order	13156
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×C₂₃×#261

Splittings

Fitting, socle, Hall	C₁₁×C₁₃×C₂₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄×C₁₁×C₂₃
Hall	C₁₃×C₂₃ ⋊ C₄×C₁₁
Hall	C₁₁×C₁₃ ⋊ C₄×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁×C₂₃	#261
commutator, hypocenter	C₁₃	C₄×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₂₃	C₄
prime radical	C₁₁×C₂₃×D₁₃	C₂
cosocle	D₁₃	C₂×C₁₁×C₂₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₁×C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 3289

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

1771 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13156, 21);

C11×C23×#261 #27190448