Finite Group Databasebeta

C2×D13⋊#349 #16806782

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D13⋊#349
unambiguous semidirect productD13⋊(C2×#349)

Splittings

SylowC13 ⋊ C22×#349

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC22×C13C23×C8
FrattiniC2×C4C23×#261
FittingC22×C13×M16C4
socleC22×C13C2×C22⋊C8
prime radicalC24×D13C8
cosocleC2×#1055C24
hypercenterC22×M16#261
hypocenterC13C22×#349
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

1262 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, 1113431);