C₁₃×#13523 #15699862

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13523
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13523

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2092
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

308 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 102 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)(14,15,17,22,27,23,43,41,19,25,35,40,18,24,34,21)(16,26,29,44,31,36,45,39,32,37,30,38,28,42,33,20);(14,16,27,28,19,32,18,31)(15,20,23,38,25,39,24,44)(17,33,43,30,35,45,34,29)(21,26,22,42,41,37,40,36);(15,21)(16,28)(17,34)(18,27)(20,36)(22,24)(23,40)(25,41)(26,44)(29,30)(31,32)(35,43)(37,38)(39,42)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6511);