Finite Group Databasebeta

#261×M64 #16791140

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

Aliases

direct product#261×M64

Splittings

FittingC13×M64 ⋊ C4
SylowC13 ⋊ C4×M64

Subgroups

subgroupG/H
center, FrattiniC16C22×#261
commutator, socleC2×C13C2×C4×C16
FittingC13×M64C4
prime radicalC22×D13C2×C16
cosocleC16×D13C23
hypercenterM64#261
hypocenterC13C4×M64
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C16 ◁ M64

250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1097789);