Finite Group Databasebeta

#15784691

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #13853

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC22×C13×#117C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×#117D13
hypocenterC13#13853
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×#117

1942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

2^8,13|a^2=h,c^2=e,d^2=g,b^a=be,c^a=cf,i^a=i^12,c^b=cg

Conjugacy classes & character table

568 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91340);