C₁₃×#10211 #15696550

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10211

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

406 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,15,22,28)(16,29,35,43)(17,36,40,31)(18,41,46,64)(19,47,52,60)(20,30,54,66)(21,27,50,63)(23,55,33,37)(24,57,61,45)(25,51,65,77)(26,44,67,70)(32,68,59,76)(34,58,69,75)(38,74,53,48)(39,72,73,42)(49,71,62,56);(14,16,21,34)(15,17,27,39)(18,42,45,31)(19,48,51,32)(20,23,44,56)(22,35,50,69)(24,58,41,29)(25,62,60,37)(26,53,66,76)(28,40,63,73)(30,68,67,38)(33,70,71,54)(36,46,72,57)(43,61,75,64)(47,55,65,49)(52,74,77,59);(14,17,21,39)(15,23,27,56)(16,30,34,67)(18,43,45,75)(19,49,51,55)(20,53,44,76)(22,40,50,73)(24,59,41,74)(25,42,60,31)(26,35,66,69)(28,33,63,71)(29,57,58,46)(32,64,48,61)(36,65,72,47)(37,52,62,77)(38,70,68,54)

Conjugacy classes & character table

325 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3199);