Finite Group Databasebeta

#261×#392 #16791703

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct product#261×#392

Splittings

FittingC13×#392 ⋊ C4
SylowC13 ⋊ C4×#392

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#392C4
prime radicalD13×#392C2
cosocleC23×D13C24
hypercenter#392#261
hypocenterC13C4×#392
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

3502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1098352);