Finite Group Databasebeta

Q8×#88034 #15783550

order3328
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C22

Aliases

direct productQ8×#88034

Splittings

SylowC13 ⋊ Q8×C32

Subgroups

subgroupG/H
center, FrattiniC2×C16C22×D13
commutatorC2×C13C22×C32
FittingQ8×C13×C16C2
socle, prime radicalC22×C13C22×C16
cosocleC2×C13×C16C23
hypercenterQ8×C16D13
hypocenterC13Q8×C32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C16 ◁ Q8×C16

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 90199);