C₁₁×#10390 #14587583

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10390
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#10390

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₁
prime radical	C₂³×D₄×C₁₁	C₂²
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁵×C₁₁ ◁ G

762 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 90 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)(14,16)(15,17)(18,19)(20,21)(22,25)(23,30,32,26)(24,27)(28,35,31,33)(29,34);(12,14)(13,16)(15,18)(17,19)(20,22)(21,25)(23,31,32,28)(24,29)(26,33,30,35)(27,34);(16,19)(20,23)(21,26)(22,28)(24,32)(25,33)(27,30)(29,31)(34,35)

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3378);