Finite Group Databasebeta

M16×#6092 #16786630

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

Aliases

direct productM16×#6092

Splittings

SylowC13 ⋊ C16×M16

Subgroups

subgroupG/H
center, FrattiniC42C22×#261
commutatorC2×C13C2×C4×C16
FittingC4×C13×M16C4
socleC22×C13C2×C4×C8
prime radicalC23×C13C4×C8
cosocleC4×#1055C23
hypercenterC4×M16#261
hypocenterC13C16×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C4×M16

306 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, 1093279);