C₁₁×#12365 #14589558

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12364
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12365

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1629
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#3291	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

346 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 78 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)(14,23)(15,26,28,43)(16,21)(17,31)(18,33)(19,25)(20,24,37,42)(22,30)(27,35,34,40)(29,38)(32,39,41,36);(12,14,16,25)(13,19,21,23)(15,24,28,42)(17,18,29,30)(20,35,37,40)(22,38,33,31)(26,36,43,39)(27,32,34,41);(12,15)(13,20)(14,24)(16,28)(17,32)(18,34)(19,35)(21,37)(22,39)(23,40)(25,42)(26,38)(27,30)(29,41)(31,43)(33,36)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5353);