Finite Group Databasebeta

D23×Q64 #15675700

order2944
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productD23×Q64

Splittings

FittingC23×Q64 ⋊ C2
SylowC23 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D23
commutator, cosocleC16×C23C23
FrattiniC16C22×D23
FittingC23×Q64C2
socleC2×C23C2×D16
prime radicalC2×D23D16
hypercenterQ64D23
hypocenterC23C2×Q64
LCSG ▷ C16×C23 ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

247 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6813);