C₁₁×#10586 #14587779

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#10586

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 350 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) = 2816

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18)(14,19,15,17)(20,21,25,29)(22,26,32,35)(23,27,24,28)(30,33,31,34)(36,37)(38,45)(39,43)(40,42)(41,46)(44,48)(47,51)(49,50);(12,14,16,15)(13,17,18,19)(20,22)(21,26)(23,31)(24,30)(25,32)(27,34)(28,33)(29,35)(36,38,39,46)(37,41,43,45)(40,49,48,47)(42,51,44,50);(12,15,16,14)(13,17,18,19)(21,27)(22,30)(23,24)(28,29)(31,32)(33,34)(37,42)(40,48)(41,50)(43,44)(45,51)(47,49)

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, 3574);