C₁₁×#12311 #14589504

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12310
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12311

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1619
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

366 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 78 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)(14,22)(15,26)(16,29)(18,32)(19,27)(20,31)(23,28)(24,40)(25,39)(30,36)(33,37)(34,43)(35,42)(38,41);(12,13,17,21)(14,18,24,34)(15,27,30,41)(16,31,29,20)(19,36,38,26)(22,37,40,42)(23,35,25,33)(28,32,39,43);(12,14)(13,18)(15,28)(16,23)(17,24)(19,37)(20,33)(21,34)(22,26)(25,29)(27,32)(30,39)(31,35)(36,40)(38,42)(41,43)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5299);