Finite Group Databasebeta

C2×#13113922 #15838613

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

Aliases

direct productC2×#13113922

Splittings

FittingC2×C13×#486 ⋊ C2
SylowC13 ⋊ C2×#1625

Subgroups

subgroupG/H
centerC23#88191
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#486C2
socleC23×C13#120
hypercenterC2×#486D13
hypocenterC13C2×#1625
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

1322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 145262);