C₁₁×#9979 #14587172

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9974
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9979

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

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

normal subgroups only

This group has 492 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) = 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)(28,29,34,38)(30,39,43,51)(31,44,48,54)(32,49,33,37)(35,42,52,41)(36,46,55,47)(40,57,58,50)(45,56,59,53);(12,14,16,21)(13,17,19,24)(15,20,22,27)(18,25,26,23)(28,30)(29,35)(31,45)(32,42)(33,41)(34,43)(36,53)(37,51)(38,52)(39,49)(40,46)(44,50)(47,58)(48,59)(54,57)(55,56);(12,15)(13,18)(14,20)(16,22)(17,23)(19,26)(21,27)(24,25)(28,31,34,48)(29,36,38,55)(30,40,43,58)(32,46,33,47)(35,50,52,57)(37,54,49,44)(39,56,51,53)(41,45,42,59)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2967);