Finite Group Databasebeta

#15789404

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #14269

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14269
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

1522 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=f,b^a=be,c^a=cf,c^b=cg,d^c=de,i^c=i^12,i^d=i^12

Conjugacy classes & character table

328 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 96053);