Finite Group Databasebeta

M16×#6127 #16727536

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productM16×#6127

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ M16×#41

Subgroups

subgroupG/H
centerC42C23×D13
commutator, socleC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×M16C2
prime radicalC22×#6127C4
cosocleC2×C4×C13C25
hypercenterC2×C4×M16D13
hypocenterC13M16×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C4×M16

2232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1034185);