C₁₁×#10497 #14587690

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10496
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10497

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#394
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

348 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 90 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)(14,21)(15,23)(16,24)(17,20)(18,22)(19,26)(25,27)(28,29)(30,33)(31,34)(32,36)(35,40)(37,41)(38,43)(39,42);(12,14)(13,18)(15,19)(16,25)(17,23)(20,27)(21,24)(22,26)(28,30,32,38)(29,33,36,43)(31,39,40,37)(34,42,35,41);(12,15,16,18,17,21,26,27)(13,14,19,22,20,23,24,25)(29,34)(31,40)(33,41)(35,36)(37,39)(42,43)

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, 3485);