Finite Group Databasebeta

M16×#6090 #15771931

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

Aliases

direct productM16×#6090

Splittings

SylowC13 ⋊ C16×M16

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D13
commutatorC2×C13C2×C4×C16
FittingC8×C13×M16C2
socleC22×C13C2×C4×C8
prime radicalC23×C13C4×C8
cosocleC4×C8×C13C23
hypercenterC8×M16D13
hypocenterC13C16×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C8×M16

306 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, 78580);