C₁₃×#10087 #15696426

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10087

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

500 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 41
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(19,24)(20,25)(21,22)(26,27,31,29)(28,34,37,41)(30,38,40,33)(32,39,35,36);(14,15)(16,17)(18,19)(20,23)(21,25)(22,24)(26,28,31,37)(27,32,29,35)(30,39,40,36)(33,41,38,34);(15,17)(18,20,23,19)(21,25,22,24)(26,29,31,27)(28,35,37,32)(30,33,40,38)(34,39,41,36)

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, 3075);