Finite Group Databasebeta

D29×Q64 #16821795

order3712
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productD29×Q64

Splittings

FittingC29×Q64 ⋊ C2
SylowC29 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D29
commutator, cosocleC16×C29C23
FrattiniC16C22×D29
FittingC29×Q64C2
socleC2×C29C2×D16
prime radicalC2×D29D16
hypercenterQ64D29
hypocenterC29C2×Q64
LCSG ▷ C16×C29 ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6813);