C₁₁×#10613 #14587806

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

Aliases

direct product

C₁₁×#10613

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)(12,13,16,23,18,22,17,21)(14,20,24,19,15,26,25,27)(28,29,33,36)(30,37,35,32)(31,38,41,39)(34,42,43,40);(12,14,16,24,18,15,17,25)(13,19,21,20,22,27,23,26)(28,30,32,29,33,35,37,36)(31,39,40,34,41,38,42,43);(12,15,18,14)(13,20,22,26)(16,24,17,25)(19,23,27,21)(28,31,33,41)(29,34,36,43)(30,38,35,39)(32,42,37,40)

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, 3601);