Finite Group Databasebeta

#261×#553 #16807626

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#261×#553

Splittings

FittingC13×#553 ⋊ C4
SylowC13 ⋊ C4×#553

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#553C4
prime radicalD13×#553C2
cosocleC22×D13C25
hypercenter#553#261
hypocenterC13C4×#553
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #553

2600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114275);