C₁₁×#10009 #14587202

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10004
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10009

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

528 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 704

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

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

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, 2997);