C₁₃×#12878 #15699217

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11669
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12878

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#418
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1824
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

362 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 138 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)(14,15,19,26,21,24,20,43)(16,27,30,48,31,22,42,47)(17,32,35,64,33,65,44,54)(18,36,39,52,41,68,40,25)(23,38,49,66,51,72,50,34)(28,56,59,77,57,73,60,75)(29,61,63,53,37,69,71,46)(45,62,74,58,55,70,76,67);(14,16)(15,22)(17,28)(18,37)(19,42)(20,30)(21,31)(23,45)(24,27)(25,53)(26,48)(29,41)(32,56)(33,57)(34,67)(35,60)(36,61)(38,70)(39,63)(40,71)(43,47)(44,59)(46,52)(49,76)(50,74)(51,55)(54,77)(58,66)(62,72)(64,75)(65,73)(68,69);(14,17,20,44,21,33,19,35)(15,23,43,50,24,51,26,49)(16,28,30,59,31,57,42,60)(18,38,40,34,41,72,39,66)(22,45,47,74,27,55,48,76)(25,54,68,65,52,64,36,32)(29,62,63,58,37,70,71,67)(46,75,61,56,53,77,69,73)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5866);