Finite Group Databasebeta

C2×M16×#1057 #16792567

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×#1057

Splittings

SylowC13 ⋊ C2×C8×M16

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC22×C13×M16C4
socleC23×C13C2×C42
prime radicalC24×C13C42
cosocleC4×Dic13C24
hypercenterC22×M16#261
hypocenterC13C2×C8×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×M16

1046 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, 1099216);