C₁₁×#12880 #14590073

order	2816
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12880

Subgroups

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

322 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 182 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) = 55
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17)(18,21)(19,20)(22,23)(24,25,27,31,28,32,37,43,29,33,38,44,39,45,49,53)(26,30,35,41,36,42,48,52,34,40,46,50,47,51,54,55);(12,13,15,14)(17,20)(21,23)(24,26)(25,30)(27,35)(28,36)(29,34)(31,41)(32,42)(33,40)(37,48)(38,46)(39,47)(43,52)(44,50)(45,51)(49,54)(53,55);(12,14,15,13)(16,18,19,22)(17,21,20,23)(26,34)(30,40)(35,46)(36,47)(41,50)(42,51)(48,54)(52,55)

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5868);