C₁₃×#13669 #15700008

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

Aliases

direct product

C₁₃×#13669

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

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

normal subgroups only

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

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, 6657);