Finite Group Databasebeta

#15755488

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

FittingC13×#1898 ⋊ C2
SylowC13 ⋊ #8534

Subgroups

subgroupG/H
centerC22#11718616
commutatorC24×C13C22×C4
FrattiniC25C22×D13
FittingC13×#1898C2
socleC22×C13#379
prime radical#13128465C2
cosocleC25×C13C23
hypercenter#1898D13
hypocenterC13#8534
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ #1898

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Polycyclic presentation:

2^8,13|a^2=f,b^a=bd,c^a=ce,d^a=dg,e^b=eh,f^b=fg,d^c=dh,i^c=i^12

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 62137);