Finite Group Databasebeta

#261×#419 #16797045

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct product#261×#419

Splittings

FittingC13×#419 ⋊ C4
SylowC13 ⋊ C4×#419

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC13×#419C4
socleC22×C13C2×C4×D4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenter#419#261
hypocenterC13C4×#419
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

1586 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, 1103694);