Finite Group Databasebeta

Q8×C22⋊#1055 #15879435

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×C22⋊#1055

Splittings

SylowC13 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC22×C4×Q8×C13C2
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC22×C4×Q8D13
hypocenterC13Q8×C22⋊C8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

1356 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, 186084);