Finite Group Databasebeta

C2×D13⋊#323 #16792792

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×D13⋊#323
unambiguous semidirect productD13⋊(C2×#323)

Splittings

SylowC13 ⋊ C22×#323

Subgroups

subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC25×D13C4
cosocleC22×Dic13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C22×#323
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

2878 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, 1099441);