C₁₁×#8799 #14585992

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8794
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#8799

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#382
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 110 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)(12,13,17,21,18,23,16,22)(14,20,24,27,25,26,15,19)(28,29,32,37,33,36,39,49)(30,38,42,51,43,34,41,52)(31,44,47,35,48,55,46,54)(40,56,57,50,45,59,58,53);(12,14,16,15,18,25,17,24)(13,19,21,20,23,27,22,26)(28,30,39,42,33,43,32,41)(29,34,49,52,36,38,37,51)(31,45,47,57,48,40,46,58)(35,53,55,59,54,50,44,56);(12,15,16,25,18,24,17,14)(13,20,21,27,23,26,22,19)(28,31)(29,35,36,54)(30,40)(32,46)(33,48)(34,50,38,53)(37,44,49,55)(39,47)(41,57)(42,58)(43,45)(51,59,52,56)

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, 1787);