Finite Group Databasebeta

Q8×#88161 #16727336

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#88161

Splittings

FittingQ8×C13×M16 ⋊ C2
SylowC13 ⋊ Q8×#131

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingQ8×C13×M16C2
prime radicalC2×#6127C23
cosocleC2×C4×C13C25
hypercenterQ8×M16D13
hypocenterC13Q8×#131
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ Q8×M16

1882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033985);