C₁₃×#13540 #15699879

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13540

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2099
prime radical	C₂³×C₁₃	#137
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

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

normal subgroups only

This group has 234 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)(14,15,18,20,19,24,21,25)(16,26,28,39,30,35,29,22)(17,31,33,41,34,23,37,36)(27,32,42,44,40,45,43,38);(14,16,21,28,19,30,18,29)(15,22,25,26,24,39,20,35)(17,32,37,44,34,45,33,38)(23,40,41,43,31,27,36,42);(14,17,18,33,19,34,21,37)(15,23,20,36,24,31,25,41)(16,27,28,42,30,40,29,43)(22,38,26,32,39,44,35,45)

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, 6528);