Finite Group Databasebeta

Q64×D281 #49097606

order35968
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ64×D281

Splittings

FittingQ64×C281 ⋊ C2
SylowC281 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D281
commutator, cosocleC16×C281C23
FrattiniC16C22×D281
FittingQ64×C281C2
socleC2×C281C2×D16
prime radicalC2×D281D16
hypercenterQ64D281
hypocenterC281C2×Q64
LCSG ▷ C16×C281 ▷ C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

2698 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6813);