C₁₁×#12109 #14589302

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12109

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#408 ◁ G

410 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 74 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)(16,19)(21,27)(22,31)(23,34)(24,25)(28,42)(29,46)(30,41)(32,48)(33,38)(35,39)(36,37)(40,43)(44,51)(45,49);(12,13)(14,16)(15,17)(18,19)(20,21,26,30)(22,28,33,45)(23,35,37,46)(24,29,25,39)(27,36,41,34)(31,43,38,44)(32,49,48,42)(40,50,51,47);(12,14)(13,16)(15,18)(17,19)(20,22)(21,28)(23,32)(24,38)(25,31)(26,33)(27,40)(29,44)(30,45)(34,47)(35,49)(36,50)(37,48)(39,43)(41,51)(42,46)

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5097);