C₁₃×#13459 #15699798

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13459
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13459

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#498
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2058
prime radical	C₂³×C₁₃	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 118 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)(16,25,27,42)(17,30)(18,23)(19,35)(20,24)(21,28,37,44)(22,34)(26,39,29,41)(31,45)(32,36,43,40)(33,38);(16,26,27,29)(17,31)(21,36,37,40)(22,38)(25,41,42,39)(28,32,44,43)(30,45)(33,34);(14,16,19,26,20,27,18,29)(15,21,23,40,24,37,35,36)(17,32,34,28,31,43,33,44)(22,39,30,25,38,41,45,42)

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, 6447);