Finite Group Databasebeta

C2×D13⋊#355 #16806903

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

Aliases

direct productC2×D13⋊#355
unambiguous semidirect productD13⋊(C2×#355)

Splittings

SylowC13 ⋊ C22×#355

Subgroups

subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#124C4
socleC22×C13C2×#99
prime radicalC22×D4×D13C4
cosocleC2×Dic26C24
hypercenterC2×#124#261
hypocenterC13C22×#355
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#124

1382 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, 1113552);