C₁₁×#12116 #14589309

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

Aliases

direct product

C₁₁×#12116

Subgroups

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

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

normal subgroups only

This group has 426 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)(14,23)(15,20)(16,28)(17,32)(18,22)(19,25)(21,30)(24,39)(26,40)(27,38)(29,34)(31,43)(33,37)(35,42)(36,41);(12,14)(13,19)(15,24)(16,29)(17,33)(18,26)(20,34)(21,37)(22,35)(23,28)(25,30)(27,42)(31,41)(32,36)(38,39)(40,43);(12,15,18,17)(13,20,22,32)(14,24,26,33)(16,30,31,27)(19,34,35,36)(21,28,38,43)(23,39,40,37)(25,41,42,29)

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, 5104);