Finite Group Databasebeta

M16×#6101 #15860912

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productM16×#6101

Splittings

SylowC13 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C22×C42
FittingC2×C4×C13×M16C2
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC2×C4×M16D13
hypocenterC13C4⋊C4×M16
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167561);