C₁₁×#10082 #14587275

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10082

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

590 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 39
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 39 points:

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

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, 3070);