C₁₁×#10668 #14587861

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#10668

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#399
prime radical	C₂³×C₁₁	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

316 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 114 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)(12,13,14,18,16,19,15,17)(20,21,24,29,25,30,26,40)(22,31,33,43,35,47,34,27)(23,36,38,46,39,28,41,45)(32,48,37,51,49,44,50,42);(13,17)(14,15)(18,19)(20,22,26,33,25,35,24,34)(21,27,40,31,30,43,29,47)(23,37,41,49,39,50,38,32)(28,44,46,42,36,48,45,51);(12,13,16,19)(14,17,15,18)(20,23,25,39)(21,28,30,36)(22,32,35,49)(24,38,26,41)(27,42,43,51)(29,45,40,46)(31,48,47,44)(33,37,34,50)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3656);