Finite Group Databasebeta

Q8×#88126 #16022343

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productQ8×#88126

Splittings

FittingC42×Q8×C13 ⋊ C2
SylowC13 ⋊ Q8×#117

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC42×Q8×C13C2
socle, cosocleC23×C13C25
prime radicalC23×D13C24
hypercenterC42×Q8D13
hypocenterC13Q8×#117
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C42×Q8

2434 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, 328992);