C₁₁×#8802 #14585995

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8603
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#8802

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#117
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#383
prime radical	C₂³×C₁₁	#117
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

258 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 110 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)(14,22,25,26)(15,18)(16,20)(17,21)(19,24,27,23)(28,29,31,34,32,35,38,41)(30,33,37,40,36,39,42,43);(13,18,21,20)(19,26,27,22)(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(12,14,15,23,17,25,16,24)(13,19,20,22,21,27,18,26)(30,36)(33,39)(37,42)(40,43)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1790);