Finite Group Databasebeta

D13×AGL(1,ℤ/16) #16016356

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

Aliases

direct productD13×AGL(1,ℤ/16)

Splittings

FittingC13×AGL(1,ℤ/16) ⋊ C2
SylowC13 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2D13×#442
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×AGL(1,ℤ/16)C2
socleC2×C13C2×#442
prime radicalD13×#509C2
cosocleC2×C8×C13C24
hypercenterAGL(1,ℤ/16)D13
hypocenterC13C2×AGL(1,ℤ/16)
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323005);