Finite Group Databasebeta

C2×D13⋊#350 #16806793

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

Aliases

direct productC2×D13⋊#350
unambiguous semidirect productD13⋊(C2×#350)

Splittings

SylowC13 ⋊ C22×#350

Subgroups

subgroupG/H
centerC2×C8C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C13×#131C4
socleC22×C13C2×C22⋊C8
prime radicalC2×#41×D13C4
cosocleC2×#1055C24
hypercenterC2×#131#261
hypocenterC13C22×#350
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113442);