Finite Group Databasebeta

#261×#344 #16785239

order3328
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#261×#344

Splittings

FittingC13×#344 ⋊ C4
SylowC13 ⋊ C4×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×#261
commutatorC22×C13C43
FrattiniC22×C4C22×#261
FittingC13×#344C4
socleC2×C13C4×#95
prime radicalC23×D13C22×C4
cosocleC22×C4×D13C23
hypercenter#344#261
hypocenterC13C4×#344
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

906 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, 1091888);