C₁₁×#8476 #14585669

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#8476

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#3512	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

678 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 142 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)(12,13,15,19,16,17,23,25)(14,20,21,27,22,18,24,26)(28,29)(30,38)(31,42,44,35)(32,45)(33,37)(34,40)(36,48)(39,54,56,59)(41,52)(43,51,47,53)(46,50)(49,55,58,57);(13,17)(15,23)(18,20)(21,24)(28,30)(29,34)(31,39)(32,46)(33,41)(35,49)(36,52)(37,50)(38,45)(40,48)(42,58)(43,57)(44,56)(47,55)(51,54)(53,59);(12,14,16,22)(13,18,17,20)(15,24,23,21)(19,27,25,26)(28,31,33,44)(29,35,37,42)(30,39,41,56)(32,47,48,43)(34,49,50,58)(36,53,45,51)(38,54,52,59)(40,57,46,55)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1464);