Finite Group Databasebeta

C2×D16×#261 #16807187

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

Aliases

direct productC2×D16×#261
unambiguous semidirect productD13⋊(C4×D16)

Splittings

FittingC2×C13×D16 ⋊ C4
SylowC13 ⋊ C2×C4×D16

Subgroups

subgroupG/H
centerC22D8×#261
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC2×C13×D16C4
socleC22×C13C4×D8
prime radicalC2×D13×D16C2
cosocleC8×D13C24
hypercenterC2×D16#261
hypocenterC13C2×C4×D16
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113836);