C₁₁×#12115 #14589308

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12114
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12115

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₁₁×#2010	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

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

normal subgroups only

This group has 422 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)(14,22)(15,26)(16,31)(17,21)(18,23)(19,30)(20,29)(24,42)(25,39)(27,37)(28,38)(32,35)(33,41)(34,43)(36,40);(12,14,17,25)(13,18,21,33)(15,27,28,43)(16,32,29,24)(19,35,36,42)(20,37,31,34)(22,38,39,26)(23,40,41,30);(15,28)(23,41)(27,43)(30,40)

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, 5103);