C₁₁×#12068 #14589261

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12068

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#442
commutator	C₈	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#1580
prime radical	C₁₁×#508	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₁₁×#346 ◁ G

204 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 352

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

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5056);