C₁₁×#9994 #14587187

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9994

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂×C₁₁×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

536 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 106 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)(14,17)(15,18)(16,19)(20,23)(21,24)(22,26)(25,27)(28,29,33,37)(30,38,41,42)(31,36,32,35)(34,39,43,40);(12,14,16,21)(13,17,19,24)(15,20,22,27)(18,25,26,23)(28,30)(29,34)(31,39)(32,40)(33,41)(35,42)(36,38)(37,43);(12,15)(13,18)(14,20)(16,22)(17,23)(19,26)(21,27)(24,25)(29,35)(30,39)(31,32)(36,37)(38,42)(40,41)

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, 2982);