Finite Group Databasebeta

C2×#13131051 #16806745

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13131051

Splittings

FittingC2×C13×M32 ⋊ C4
SylowC13 ⋊ C22×#347

Subgroups

subgroupG/H
centerC2×C4C2×C4×#261
commutatorC4×C13C22×C42
FrattiniC8C23×#261
FittingC2×C13×M32C4
socleC22×C13C2×#97
prime radicalC23×D13M16
cosocleC8×D13C24
hypercenterC2×M32#261
hypocenterC13C22×#347
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×M32

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113394);