C₁₃×#9944 #15696283

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9938
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9944

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

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

normal subgroups only

This group has 654 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)(14,15,18,23)(16,25,27,37)(17,29,32,21)(19,24,33,22)(20,30,35,26)(28,41,44,40)(31,39,42,38)(34,43,36,45);(14,16,19,28)(15,20,24,36)(17,30,31,45)(18,27,33,44)(21,37,38,40)(22,34,23,35)(25,39,41,29)(26,42,43,32);(17,31)(20,34)(21,38)(25,37)(26,43)(29,39)(30,45)(32,42)(35,36)(40,41)

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, 2932);