Finite Group Databasebeta

← Prev (#15721318) Next (#15721320) →

C13×#34980 #15721319

order3328
nilpotency class2
isoclinismisoclinic class of #34980
automorphism?
homologyAbelianization (H1) = C25×C13 · Schur multiplier (H2) = C210

Aliases

direct productC13×#34980

Subgroups

subgroupG/H
center, socleC23×C13C25
commutator, Frattini, cosocleC23C25×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

7786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 416

A minimal faithful permutation representation — 5 generators on 29 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,21)(24,28)(27,29);(18,19)(20,21)(23,26)(27,29);(14,15)(16,17)(18,19)(20,21)(22,23)(24,27)(25,26)(28,29);(22,23)(24,27)(25,26)(28,29);(22,24)(23,27)(25,28)(26,29)

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 27968);