C₁₃×#10339 #15696678

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10336
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10339

Subgroups

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

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

normal subgroups only

This group has 738 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)(14,15,18,23)(16,20,27,34)(17,21,28,36)(19,24,30,22)(25,39,40,35)(26,32,42,33)(29,38,43,37)(31,44,45,41);(14,16,18,27)(15,20,23,34)(17,25,28,40)(19,26,30,42)(21,35,36,39)(22,33,24,32)(29,41,43,44)(31,38,45,37);(14,17,19,29)(15,21,24,38)(16,25,26,41)(18,28,30,43)(20,31,32,39)(22,37,23,36)(27,40,42,44)(33,35,34,45)

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, 3327);