C₁₁×#12309 #14589502

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12307
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12309

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1616
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₁₁×#469	C₂²
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

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

normal subgroups only

This group has 280 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)(12,13,18,22,17,23,16,20)(14,24,26,41,28,42,27,38)(15,29,32,39,31,37,33,21)(19,34,35,25,36,30,40,43);(12,14)(13,19)(15,30)(16,26)(17,28)(18,27)(20,35)(21,38)(22,40)(23,36)(24,37)(25,32)(29,42)(31,34)(33,43)(39,41);(13,20,23,22)(15,31)(19,35,36,40)(21,37,39,29)(24,41,42,38)(25,43)(30,34)(32,33)

Conjugacy classes & character table

275 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5297);