Finite Group Databasebeta

#261×#410 #16796966

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#261×#410

Splittings

FittingC13×#410 ⋊ C4
SylowC13 ⋊ C4×#410

Subgroups

subgroupG/H
centerC4C22⋊C4×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC13×#410C4
socleC2×C13C2×C4×C22⋊C4
prime radicalC2×#41×D13C22
cosocleC23×D13C24
hypercenter#410#261
hypocenterC13C4×#410
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

1666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 1103615);