C₁₃×#13515 #15699854

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13515

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

298 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 130 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)(18,19)(20,25)(21,23)(22,24)(26,27,30,35,28,36,37,41,29,34,38,40,31,32,39,33);(14,15)(16,17)(18,20,22,21)(19,23,24,25)(26,28,29,31)(27,32,34,36)(30,37,38,39)(33,40,41,35);(15,17)(18,21,22,20)(19,23,24,25)(27,33)(28,31)(30,39)(32,35)(34,41)(36,40)(37,38)

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6503);