C₁₃×#13356 #15699695

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13353
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13356

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#585	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

676 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,15,20,25)(16,26,30,48)(17,31,34,50)(18,35,38,23)(19,39,41,24)(21,36,44,28)(22,40,47,33)(27,53,56,77)(29,59,61,52)(32,64,66,63)(37,49,71,68)(42,73,45,76)(43,58,72,69)(46,65,67,70)(51,60,74,55)(54,62,57,75);(14,16)(15,21)(17,27)(18,36)(19,29)(20,30)(22,45)(23,48)(24,43)(25,44)(26,35)(28,38)(31,62)(32,57)(33,55)(34,56)(37,69)(39,72)(40,60)(41,61)(42,47)(46,74)(49,59)(50,75)(51,67)(52,68)(53,64)(54,66)(58,71)(63,77)(65,76)(70,73);(14,17,20,34)(15,22,25,47)(16,27,30,56)(18,32,38,66)(19,40,41,33)(21,42,44,45)(23,46,35,67)(24,50,39,31)(26,51,48,74)(28,57,36,54)(29,60,61,55)(37,70,71,65)(43,62,72,75)(49,64,68,63)(52,77,59,53)(58,73,69,76)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6344);