C₁₃×#13513 #15699852

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13513

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#482
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2085
prime radical	C₂³×C₁₃	#137
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 228 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

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

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, 6501);