C₁₁×#9007 #14586200

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9007

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#386
prime radical	C₁₁×#3150	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

502 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 1408

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1995);