C₁₁×#9991 #14587184

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#9991

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 51
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,17)(18,19)(20,21,26,31)(22,32,36,43)(23,37,41,46)(24,30,25,29)(27,35,44,34)(28,39,47,40)(33,42,49,50)(38,51,48,45);(16,19)(20,22,26,36)(21,27,31,44)(23,38,41,48)(24,35,25,34)(28,45,47,51)(29,43,30,32)(33,40,49,39)(37,50,46,42);(12,14)(13,16)(15,18)(17,19)(20,23,26,41)(21,28,31,47)(22,33,36,49)(24,39,25,40)(27,42,44,50)(29,46,30,37)(32,45,43,51)(34,38,35,48)

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, 2979);