C₁₁×#8463 #14585656

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#8463

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₁₁×#3493	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

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

normal subgroups only

This group has 718 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) = 704

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

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

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, 1451);