Finite Group Databasebeta

#261×#340 #16785209

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

Aliases

direct product#261×#340

Splittings

FittingC13×#340 ⋊ C4
SylowC13 ⋊ C4×#340

Subgroups

subgroupG/H
centerC23D4×#261
commutatorC4×C13C43
FrattiniC22×C4C22×#261
FittingC13×#340C4
socleC23×C13C4×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#340#261
hypocenterC13C4×#340
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1091858);