C₁₃×#13522 #15699861

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13522
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13522

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2088
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#137
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

240 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 106 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)(14,15,21,34,32,17,19,23,20,25,36,31,18,24,33,41)(16,26,35,38,29,40,28,42,30,39,44,45,27,22,37,43);(14,16,18,27,20,30,32,29)(15,22,17,26,25,40,24,39)(19,28,21,35,33,37,36,44)(23,38,31,42,41,45,34,43);(14,17,18,25,20,24,32,15)(16,22,27,26,30,40,29,39)(19,23,21,31,33,41,36,34)(28,43,35,38,37,42,44,45)

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, 6510);