C₁₃×#9983 #15696322

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9983

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₁₃×#2815	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

602 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,25)(17,29)(21,37)(22,26)(23,34)(24,36)(27,33)(28,44)(30,31)(35,39)(38,41)(40,43)(42,45);(14,15,19,24)(16,26,27,43)(17,21,31,39)(18,22,32,40)(20,33,36,25)(23,29,41,30)(28,35,44,37)(34,42,38,45);(15,21)(16,27)(17,30)(20,34)(22,23)(24,39)(25,33)(26,37)(28,45)(29,31)(35,43)(36,38)(40,41)(42,44)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2971);