Finite Group Databasebeta

C4×M16×#261 #16796726

order3328
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productC4×M16×#261

Splittings

FittingC4×C13×M16 ⋊ C4
SylowC13 ⋊ C42×M16

Subgroups

subgroupG/H
centerC42C22×#261
commutatorC2×C13C2×C43
FrattiniC2×C4C23×#261
FittingC4×C13×M16C4
socleC22×C13C22×C42
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenterC4×M16#261
hypocenterC13C42×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C4×M16

1734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1103375);