Finite Group Databasebeta

#261×#342 #16785231

order3328
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct product#261×#342

Splittings

FittingC13×#342 ⋊ C4
SylowC13 ⋊ C4×#342

Subgroups

subgroupG/H
centerC22C22⋊C4×#261
commutatorC22×C13C43
FrattiniC24C22×#261
FittingC13×#342C4
socleC22×C13C4×C22⋊C4
prime radical, cosocleC24×D13C23
hypercenter#342#261
hypocenterC13C4×#342
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #342

1482 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, 1091880);