C₁₁×#10012 #14587205

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#10012

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#392
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

734 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 35
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,18)(16,19)(20,21)(22,28)(23,31)(24,27)(25,29)(26,33)(30,35)(32,34);(13,17)(14,15)(18,19)(20,22)(21,25)(23,32)(24,30)(26,35)(27,34)(28,31)(29,33);(13,18)(14,15)(17,19)(25,34)(28,35)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3000);