C₁₁×#7834 #14585027

order	2816
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#7834

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 ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 396 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) = 1408

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

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 822);