Finite Group Databasebeta

D31×Q64 #16848014

order3968
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productD31×Q64

Splittings

FittingC31×Q64 ⋊ C2
SylowC31 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D31
commutator, cosocleC16×C31C23
FrattiniC16C22×D31
FittingC31×Q64C2
socleC2×C31C2×D16
prime radicalC2×D31D16
hypercenterQ64D31
hypocenterC31C2×Q64
LCSG ▷ C16×C31 ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 6813);