C₁₁×#10135 #14587328

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10128
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10135

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

434 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 59
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11)(14,20)(15,22)(17,25)(18,23)(21,24)(26,27)(28,29,34,39)(30,40,43,51)(31,36,47,54)(32,38,33,37)(35,44,50,42)(41,56,57,52)(45,59,58,49)(46,55,48,53);(12,13,16,19)(14,17,21,26)(15,23,22,18)(20,27,24,25)(28,30)(29,35)(31,45)(32,44)(33,42)(34,43)(36,52)(37,51)(38,40)(39,50)(41,46)(47,58)(48,57)(49,53)(54,56)(55,59);(12,14)(13,17)(15,24)(16,21)(18,27)(19,26)(20,22)(23,25)(28,31,34,47)(29,36,39,54)(30,41,43,57)(32,46,33,48)(35,49,50,59)(37,53,38,55)(40,52,51,56)(42,45,44,58)

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, 3123);