C₁₁×#10614 #14587807

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#10614

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 276 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) = 43
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 43 points:

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

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, 3602);