Finite Group Databasebeta

Q16×#6122 #16796343

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productQ16×#6122

Splittings

SylowC13 ⋊ M16×Q16

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC22×C13×Q16C4
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC4×Dic13C24
hypercenterC22×Q16#261
hypocenterC13M16×Q16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1102992);