C₁₃×#13655 #15699994

order	3328
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13655

Subgroups

	subgroup	G/H
center	C₈×C₁₃	D₁₆
commutator	C₁₆	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	C₄×D₁₆
prime radical	C₁₃×#2262	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₄×C₁₃×C₁₆ ◁ G

186 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 86 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)(14,15,19,25,21,27,42,26)(16,28,31,58,33,59,32,64)(17,23,35,50,36,51,20,43)(18,37,39,67,41,69,73,68)(22,45,47,63,49,62,56,30)(24,34,53,65,55,66,54,40)(29,57,60,76,61,77,44,52)(38,46,70,74,72,75,71,48);(14,16)(15,22)(17,29)(18,38)(19,31)(20,44)(21,33)(23,46)(24,52)(25,47)(26,56)(27,49)(28,37)(30,40)(32,42)(34,45)(35,60)(36,61)(39,70)(41,72)(43,48)(50,74)(51,75)(53,57)(54,77)(55,76)(58,67)(59,69)(62,66)(63,65)(64,68)(71,73);(14,17,19,35,21,36,42,20)(15,23,25,50,27,51,26,43)(16,29,31,60,33,61,32,44)(18,34,39,65,41,66,73,40)(22,46,47,74,49,75,56,48)(24,37,53,67,55,69,54,68)(28,57,58,76,59,77,64,52)(30,38,45,70,63,72,62,71)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6643);