Finite Group Databasebeta

#15784652

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #13847

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1438C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenter#1438D13
hypocenterC13#13847
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1438

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

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

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91301);