C₁₁×#12465 #14589658

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12465

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1677
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#2213	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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)(13,19)(14,24)(15,20)(16,31)(17,30)(22,42)(23,32)(25,26)(27,29)(28,36)(33,38)(34,35)(37,43)(39,40);(12,13,20,35,17,22,16,32,18,23,31,42,30,34,15,19)(14,21,36,38,26,39,25,37,28,41,24,43,27,40,29,33);(12,14)(13,21)(15,29)(16,25)(17,26)(18,28)(19,33)(20,36)(22,39)(23,41)(24,31)(27,30)(32,37)(34,40)(35,38)(42,43)

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5453);