C₁₃×#13608 #15699947

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13605
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13608

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2127
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	#124	C₂³×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#536 ◁ G

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

normal subgroups only

This group has 308 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)(16,26,29,53)(17,22)(18,34,36,68)(19,38,40,24)(20,25)(21,28,42,59)(23,37)(27,52,56,74)(30,49,39,54)(31,62,35,67)(32,64,66,47)(33,48)(41,58,72,77)(43,60,44,61)(45,55,73,76)(46,63)(50,69)(51,70)(57,71,65,75);(14,16,20,30)(15,21,25,44)(17,27,33,57)(18,28,36,61)(19,39,40,29)(22,45,48,41)(23,49,51,26)(24,42,38,43)(31,55,35,58)(32,65,66,56)(34,54,68,53)(37,59,70,60)(46,71,50,52)(47,73,64,72)(62,75,67,74)(63,76,69,77);(14,17,20,33)(15,22,25,48)(16,27,30,57)(18,35,36,31)(19,32,40,66)(21,41,44,45)(23,50,51,46)(24,47,38,64)(26,52,49,71)(28,58,61,55)(29,56,39,65)(34,67,68,62)(37,69,70,63)(42,72,43,73)(53,74,54,75)(59,77,60,76)

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, 6596);