C₁₁×#7309 #14584502

order	2816
nilpotency class	4
isoclinism	isoclinic class of #7307
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#7309

Subgroups

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

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

normal subgroups only

This group has 470 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)(22,30,32,41)(23,34,36,27)(24,28)(25,29)(26,31)(33,45,48,51)(35,40)(37,44,46,42)(38,43)(39,47)(49,50);(12,14)(13,16,17,18)(15,19)(20,22,24,33,25,32,38,48)(21,26,28,39,29,40,43,50)(23,35,37,49,36,31,46,47)(27,41,42,51,34,30,44,45)

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, 297);