Finite Group Databasebeta

C2×#13129772 #16786768

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13129772

Splittings

SylowC13 ⋊ C2×#1322

Subgroups

subgroupG/H
centerC22×C4C22⋊#261
commutatorC22×C13C22×C16
FrattiniC22×C4C22×#261
FittingC22×C42×C13C4
socleC23×C13C22⋊C8
prime radicalC24×C13C2×C8
cosocleC22×#1055C23
hypercenterC22×C42#261
hypocenterC13C2×#1322
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

466 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, 1093417);