C₁₃×#13671 #15700010

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

Aliases

direct product

C₁₃×#13671

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
prime radical	C₁₃×#3415	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#131 ◁ C₁₃×#504 ◁ G

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

normal subgroups only

This group has 284 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)(14,15,21,28)(16,29,33,58)(17,34,40,67)(18,27,20,25)(19,43,45,59)(22,46,50,30)(23,41,52,31)(24,53,57,38)(26,42,61,36)(32,64,65,51)(35,60,70,77)(37,47,39,66)(44,54,74,76)(48,63,62,69)(49,73,75,68)(55,72,56,71);(14,16)(15,22)(17,35)(18,31)(19,44)(20,41)(21,33)(23,47)(24,54)(25,48)(26,60)(27,62)(28,50)(29,34)(30,38)(32,36)(37,68)(39,73)(40,70)(42,65)(43,49)(45,74)(46,53)(51,56)(52,66)(55,64)(57,76)(58,67)(59,75)(61,77)(63,72)(69,71);(14,16)(15,23)(17,30)(18,41)(19,32)(20,31)(21,33)(22,47)(24,49)(25,58)(26,51)(27,29)(28,52)(34,62)(35,38)(36,44)(37,69)(39,63)(40,46)(42,74)(43,54)(45,65)(48,67)(50,66)(53,70)(55,77)(56,60)(57,75)(59,76)(61,64)(68,71)(72,73)

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, 6659);