Finite Group Databasebeta

Q64×D269 #46813188

order34432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ64×D269

Splittings

FittingQ64×C269 ⋊ C2
SylowC269 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D269
commutator, cosocleC16×C269C23
FrattiniC16C22×D269
FittingQ64×C269C2
socleC2×C269C2×D16
prime radicalC2×D269D16
hypercenterQ64D269
hypocenterC269C2×Q64
LCSG ▷ C16×C269 ▷ C8×C269 ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

2584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6813);