C₁₁×#10666 #14587859

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10666

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#399
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 354 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)(12,13,17,18,16,14,15,19)(20,21,26,30,25,31,24,29)(22,32,40,27,35,43,34,42)(23,28,38,47,39,46,37,45)(33,48,36,51,50,44,49,41);(12,14,16,13)(15,19,17,18)(20,22,24,40,25,35,26,34)(21,27,29,43,31,42,30,32)(23,36,37,50,39,49,38,33)(28,44,45,41,46,48,47,51);(13,18)(14,19)(15,17)(20,23)(21,28)(22,33)(24,37)(25,39)(26,38)(27,41)(29,45)(30,47)(31,46)(32,44)(34,49)(35,50)(36,40)(42,51)(43,48)

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, 3654);