C₁₃×#13441 #15699780

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13441

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 378 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) = 81
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,29)(20,30,34,62)(21,35,40,53)(22,41,45,60)(23,46,43,28)(25,48,51,32)(26,37,55,38)(27,56,58,44)(31,63,66,79)(33,67,47,57)(36,61,64,52)(39,75,72,69)(42,59,77,50)(49,70,78,65)(54,74,68,73)(71,80,76,81);(18,20,24,34)(19,25,29,51)(21,36,40,64)(22,42,45,77)(23,47,43,33)(26,52,55,61)(27,57,58,67)(28,59,46,50)(30,60,62,41)(31,37,66,38)(32,56,48,44)(35,49,53,78)(39,76,72,71)(54,81,68,80)(63,69,79,75)(65,74,70,73);(15,17)(18,21,22,37,43,72,56,74,24,40,45,38,23,39,44,73)(19,26,27,53,46,68,60,69,29,55,58,35,28,54,41,75)(20,31,32,64,47,70,77,71,34,66,48,36,33,65,42,76)(25,49,30,61,59,79,67,80,51,78,62,52,50,63,57,81)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6429);