C₁₁×#10627 #14587820

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10370
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10627

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#397
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 330 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)(20,21)(22,30,33,43)(23,27)(24,28)(25,29)(26,32,40,37)(31,46,34,45)(35,41)(36,42)(38,44)(39,48,50,47)(49,51);(12,13)(14,16)(15,18)(17,19)(20,22)(21,26)(23,34)(24,37)(25,33)(27,39)(28,43)(29,40)(30,44)(31,36)(32,38)(35,47)(41,46)(42,50)(45,51)(48,49);(13,16)(14,19)(17,18)(20,23,24,35,25,36,38,49)(21,27,28,41,29,42,44,51)(22,31,32,47,33,34,37,48)(26,39,30,45,40,50,43,46)

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, 3615);