Finite Group Databasebeta

← Prev (#15701656) Next (#15701658) →

C13×#15318 #15701657

order3328
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C13 · Schur multiplier (H2) = C26

Aliases

direct productC13×#15318

Subgroups

subgroupG/H
center, socle, prime radicalC24×C13C24
commutator, Frattini, cosocleC24C24×C13
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

1722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 3328

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 8306);