C₁₁×#8492 #14585685

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#8492

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#379
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

692 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 142 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 — 3 generators on 51 points:

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

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, 1480);