Finite Group Databasebeta

C2×D13⋊#352 #16806806

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D13⋊#352
unambiguous semidirect productD13⋊(C2×#352)

Splittings

FittingC2×C13×#123 ⋊ C4
SylowC13 ⋊ C22×#352

Subgroups

subgroupG/H
centerC22D13⋊#99
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C13×#123C4
socleC22×C13C2×#99
prime radicalC22×D4×D13C22
cosocleC2×C22⋊D13C24
hypercenterC2×#123#261
hypocenterC13C22×#352
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

1486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113455);