C₁₁×#12044 #14589237

order	2816
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12044

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator	C₈	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle, prime radical	C₂²×C₁₁	C₄×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ C₈²×C₁₁ ◁ G

222 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 2816

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

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5032);