C₁₁×#10391 #14587584

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10390
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#10391

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁵×C₁₁ ◁ G

542 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 352

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

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

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3379);