C₁₁×#7306 #14584499

order	2816
nilpotency class	4
isoclinism	isoclinic class of #7304
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#7306

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#342
commutator	C₂⁴	C₄²×C₁₁
Frattini, cosocle	C₂²×#41	C₂²×C₁₁
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂⁴ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₁₁×#41 ◁ G

456 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 78 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)(14,18)(15,17)(16,19)(20,21,24,29,26,31,25,30)(22,32,34,47,36,49,35,48)(23,37,38,46,39,28,40,44)(27,41,42,33,43,50,45,51);(12,14)(13,16,17,18)(15,19)(20,22,25,35,26,36,24,34)(21,27,30,42,31,43,29,45)(23,33,38,50,39,51,40,41)(28,32,44,48,37,49,46,47)

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, 294);