Finite Group Databasebeta

#261×#388 #16791539

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

Aliases

direct product#261×#388

Splittings

FittingC13×#388 ⋊ C4
SylowC13 ⋊ C4×#388

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#388C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenter#388#261
hypocenterC13C4×#388
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

2134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1098188);