C₁₃×#13524 #15699863

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13523
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13524

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2092
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 288 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)(14,15,18,24,43,26,47,59,21,28,19,25,20,27,44,60)(16,29,31,63,32,61,45,51,34,65,70,50,33,57,41,22)(17,35,37,55,48,58,46,23,40,53,38,54,39,62,42,56)(30,49,66,71,36,72,73,77,68,75,74,76,67,52,69,64);(14,16,20,32,21,34,43,33)(15,22,27,63,28,51,26,50)(17,36,39,68,40,67,48,30)(18,41,44,31,19,45,47,70)(23,52,55,49,56,72,54,75)(24,57,60,29,25,61,59,65)(35,71,62,77,53,76,58,64)(37,66,42,73,38,74,46,69);(14,17,21,40)(15,23,28,56)(16,30,34,68)(18,42,19,46)(20,48,43,39)(22,49,51,75)(24,58,25,62)(26,55,27,54)(29,64,65,77)(31,69,70,73)(32,67,33,36)(35,60,53,59)(37,47,38,44)(41,66,45,74)(50,72,63,52)(57,71,61,76)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6512);