C₁₁×#7261 #14584454

order	2816
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7261

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#102
commutator	C₂×C₈	C₄²×C₁₁
Frattini, cosocle	C₂³×C₈	C₂²×C₁₁
socle	C₂²×C₁₁	#340
prime radical	C₂⁴×C₁₁	Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

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

normal subgroups only

This group has 320 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) = 51
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,18)(17,19)(20,21,24,29,26,30,25,40)(22,31,33,47,34,48,41,45)(23,35,37,46,39,50,38,28)(27,36,42,49,44,51,43,32);(13,16,18,17)(20,22,24,33,26,34,25,41)(21,27,29,42,30,44,40,43)(23,36,37,49,39,51,38,32)(28,45,35,31,46,47,50,48)

Conjugacy classes & character table

638 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 249);