C₁₁×#10513 #14587706

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10512
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10513

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#3245	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

388 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,21)(15,17)(16,20)(18,22)(19,24)(23,26)(25,27)(28,29)(30,38)(31,36)(32,35)(33,37)(34,40)(39,43)(41,42);(13,17)(14,22)(15,24)(18,26)(19,20)(21,25)(28,30)(29,34)(31,40)(32,41)(33,39)(35,43)(36,38)(37,42);(12,14,15,23,16,22,24,27)(13,18,19,26,20,21,17,25)(29,35)(30,39)(32,33)(36,37)(40,41)(42,43)

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, 3501);