Finite Group Databasebeta

#15789604

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

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #14292

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×C22⋊Q8C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×C22⋊Q8D13
hypocenterC13#14292
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

1782 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=eg,b^a=be,c^a=cf,i^a=i^12,c^b=cg,d^c=de

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 96253);