Finite Group Databasebeta

Q8×#88169 #16743517

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#88169

Splittings

FittingQ8×C13×SD16 ⋊ C2
SylowC13 ⋊ Q8×#137

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingQ8×C13×SD16C2
socleC22×C13C23×D4
prime radicalC2×#6129C23
hypercenterQ8×SD16D13
hypocenterC13Q8×#137
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q8×SD16

1782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1050166);