Finite Group Databasebeta

M32×#1057 #16786578

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

Aliases

direct productM32×#1057

Splittings

SylowC13 ⋊ C8×M32

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×#261
commutatorC2×C13C2×C82
FittingC2×C13×M32C4
socleC22×C13C2×C4×C8
prime radicalC23×C13C4×C8
cosocleC8×Dic13C23
hypercenterC2×M32#261
hypocenterC13C8×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×M32

354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1093227);