Finite Group Databasebeta

Q16×#6094 #15834374

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

Aliases

direct productQ16×#6094

Splittings

FittingC8×C13×Q16 ⋊ C2
SylowC13 ⋊ M16×Q16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×Q16C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenterC8×Q16D13
hypocenterC13M16×Q16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 141023);