Finite Group Databasebeta

#261×#542 #16807556

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

Aliases

direct product#261×#542

Splittings

FittingC13×#542 ⋊ C4
SylowC13 ⋊ C4×#542

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#542C4
prime radicalD13×#121C22
cosocleC22×D13C25
hypercenter#542#261
hypocenterC13C4×#542
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #542

2294 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, 1114205);