C₁₃×#13670 #15700009

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13669
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13670

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#131 ◁ C₁₃×#504 ◁ G

278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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)(15,22)(16,27)(17,31)(18,20)(19,33)(23,45)(24,50)(25,51)(26,44)(28,55)(29,59)(30,37)(32,39)(34,62)(35,61)(36,63)(38,40)(41,43)(42,46)(47,56)(48,70)(49,69)(52,66)(53,57)(58,76)(60,71)(64,68)(65,75)(72,74)(73,77);(14,15)(16,23)(17,32)(18,24)(19,39)(20,41)(21,26)(22,31)(25,33)(27,46)(28,56)(29,60)(30,49)(34,51)(35,66)(36,64)(37,48)(38,52)(40,68)(42,57)(43,61)(44,63)(45,55)(47,54)(50,62)(53,71)(58,77)(59,72)(65,74)(67,73)(69,76)(70,75);(14,16,21,30)(15,23,26,49)(17,28,36,58)(18,37,20,27)(19,29,40,59)(22,42,44,70)(24,48,41,46)(25,47,52,73)(31,57,63,75)(32,56,64,77)(33,54,38,67)(34,65,35,53)(39,60,68,72)(43,69,50,45)(51,74,66,71)(55,61,76,62)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6658);