C₁₁×#9992 #14587185

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9992

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₁₁×#3192	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

562 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 704

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

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, 2980);