Finite Group Databasebeta

Q8×#88036 #16791490

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

Aliases

direct productQ8×#88036

Splittings

SylowC13 ⋊ Q8×C32

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×#261
commutatorC2×C13C22×C32
FittingC8×Q8×C13C4
socle, prime radicalC22×C13C22×C16
cosocleC2×#6090C23
hypercenterC8×Q8#261
hypocenterC13Q8×C32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C8×Q8

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1098139);