C₁₁×#12166 #14589359

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

Aliases

direct product

C₁₁×#12166

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#2184	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#424 ◁ G

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

normal subgroups only

This group has 362 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)(20,21)(22,33)(23,27)(24,31)(25,30)(26,32)(28,35)(29,37)(34,47)(36,48)(38,45)(39,43)(40,44)(41,46)(42,51)(49,50);(12,13)(14,16)(15,17)(18,19)(21,27)(23,37)(24,25)(28,42)(29,31)(30,43)(32,44)(33,47)(34,50)(35,41)(38,51)(39,40)(45,48)(46,49);(12,14,15,18)(13,16,17,19)(20,22)(21,28)(23,38)(24,41)(25,35)(26,36)(27,42)(29,47)(30,48)(31,33)(32,46)(34,40)(37,51)(39,50)(43,45)(44,49)

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, 5154);