C₁₁×#23469 #14600662

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23444
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₁×#23469

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂³×D₄×C₁₁	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

1402 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 334 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 — 4 generators on 35 points:

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16457);