Finite Group Databasebeta

M16×#6105 #15834355

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×#6105

Splittings

SylowC13 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingD4×C13×M16C2
socleC22×C13C2×C4×D4
prime radicalC22×D4×C13C2×C4
cosocleC42×C13C24
hypercenterD4×M16D13
hypocenterC13M16×SD16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 141004);