C₁₁×#9414 #14586607

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9385
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#9414

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂×C₁₁×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

552 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2402);