Finite Group Databasebeta

M32×#1055 #15771896

order3328
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8

Aliases

direct productM32×#1055

Splittings

SylowC13 ⋊ C8×M32

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D13
commutatorC2×C13C2×C82
FittingC4×C13×M32C2
socleC22×C13C2×C4×C8
prime radicalC23×C13C4×C8
cosocleC4×C8×C13C23
hypercenterC4×M32D13
hypocenterC13C8×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C4×M32

354 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, 78545);