Finite Group Databasebeta

C2×#13116036 #15890388

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116036

Splittings

SylowC13 ⋊ C2×#2036

Subgroups

subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C2×D4
prime radicalC25×C13D4
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2036
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

1662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 197037);