C₁₁×#10121 #14587314

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10121

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#3153	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 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)(13,16)(14,18)(17,19)(20,21)(22,31)(23,36)(24,41)(25,29)(26,30)(27,33)(28,39)(32,49)(34,44)(35,43)(37,48)(38,47)(40,46)(42,50)(45,51);(14,18)(16,19)(20,22)(21,27)(23,37)(24,34)(25,33)(26,35)(28,45)(29,43)(30,44)(31,41)(32,38)(36,42)(39,50)(40,51)(46,49)(47,48);(12,13)(14,19)(15,17)(16,18)(20,23,26,40)(21,28,30,47)(22,32,35,50)(24,38,25,39)(27,42,44,49)(29,46,41,36)(31,48,43,45)(33,37,34,51)

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, 3109);