C₁₁×#10635 #14587828

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10631
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10635

Subgroups

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

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

normal subgroups only

This group has 294 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)(13,16)(17,19)(20,21,25,30,26,31,24,29)(22,32,35,27,36,43,34,44)(23,37,39,45,40,46,41,28)(33,48,49,51,38,42,50,47);(13,17)(15,18)(16,19)(20,22,26,36)(21,27,31,44)(23,38,40,33)(24,35,25,34)(28,42,45,48)(29,43,30,32)(37,51,46,47)(39,49,41,50);(12,13)(14,16)(15,19)(17,18)(20,23,24,39,26,40,25,41)(21,28,29,37,31,45,30,46)(22,33,34,49,36,38,35,50)(27,42,32,47,44,48,43,51)

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, 3623);