C₁₁×#12308 #14589501

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

Aliases

direct product

C₁₁×#12308

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1616
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

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

normal subgroups only

This group has 274 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)(12,13,16,19,17,22,33,21)(14,23,25,38,26,41,32,40)(15,27,30,20,31,37,29,39)(18,28,35,24,36,42,34,43);(12,14,17,26)(13,18,22,36)(15,28,31,42)(16,32,33,25)(19,34,21,35)(20,38,39,40)(23,27,41,37)(24,30,43,29);(13,19,22,21)(18,34,36,35)(20,27,39,37)(23,38,41,40)

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, 5296);