Finite Group Databasebeta

Dic13×M64 #15783094

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productDic13×M64

Splittings

SylowC13 ⋊ C4×M64

Subgroups

subgroupG/H
center, FrattiniC2×C16C22×D13
commutatorC2×C13C2×C4×C16
FittingC2×C13×M64C2
socleC22×C13C22×C16
prime radicalC23×C13C2×C16
cosocleC2×C13×C16C23
hypercenterC2×M64D13
hypocenterC13C4×M64
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C16 ◁ C2×M64

250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 89743);