C₁₁×#9985 #14587178

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9985

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

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

normal subgroups only

This group has 502 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) = 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)(14,17)(15,18)(16,19)(20,23)(21,24)(22,26)(25,27)(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);(12,14,16,21)(13,17,19,24)(15,20,22,27)(18,25,26,23)(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);(12,15)(13,18)(14,20)(16,22)(17,23)(19,26)(21,27)(24,25)(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

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2973);