C₁₁×#9982 #14587175

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#9982

Subgroups

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

722 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 98 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)(22,32,35,43)(23,28,39,46)(24,30,25,29)(27,36,42,34)(33,48,49,44)(37,51,50,41)(38,47,40,45);(16,19)(20,22)(21,27)(23,37)(24,36)(25,34)(26,35)(28,44)(29,43)(30,32)(31,42)(33,38)(39,50)(40,49)(41,45)(46,48)(47,51);(12,14)(13,16)(15,18)(17,19)(20,23,26,39)(21,28,31,46)(22,33,35,49)(24,38,25,40)(27,41,42,51)(29,45,30,47)(32,44,43,48)(34,37,36,50)

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, 2970);