Finite Group Databasebeta

C2×#13116731 #16016357

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13116731

Splittings

FittingC2×C13×#360 ⋊ C2
SylowC13 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22#11718446
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C13×#360C2
socleC22×C13#442
prime radicalC2×#11718854C2
cosocleC2×C8×C13C24
hypercenterC2×#360D13
hypocenterC13C2×AGL(1,ℤ/16)
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323006);