Finite Group Databasebeta

Q8×#88168 #16743498

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

Aliases

direct productQ8×#88168

Splittings

FittingQ8×C13×SD16 ⋊ C2
SylowC13 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingQ8×C13×SD16C2
socleC22×C13C23×D4
prime radicalC2×#88168C22
hypercenterQ8×SD16D13
hypocenterC13Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q8×SD16

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1050147);