C₁₁×#10126 #14587319

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10126

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 454 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)(12,13,17,14)(15,22,23,27)(16,21,26,19)(18,25,20,24)(28,29,33,36)(30,37,39,42)(31,41,32,35)(34,40,43,38);(12,14,17,13)(15,20,23,18)(16,19,26,21)(22,25,27,24)(28,30,33,39)(29,34,36,43)(31,40,32,38)(35,42,41,37);(12,15)(13,18)(14,20)(16,25)(17,23)(19,27)(21,22)(24,26)(30,38)(31,32)(34,42)(35,41)(37,43)(39,40)

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3114);