Finite Group Databasebeta

Q8×#88052 #16016433

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productQ8×#88052

Splittings

SylowC13 ⋊ Q8×M32

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D13
commutator, socleC22×C13C23×C8
FittingC2×C8×Q8×C13C2
prime radicalC23×C13C22×C8
cosocleC2×C8×C13C24
hypercenterC2×C8×Q8D13
hypocenterC13Q8×M32
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×C8×Q8

530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323082);