Finite Group Databasebeta

C2×#13130876 #16798677

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13130876
unambiguous semidirect productD13⋊#1908

Splittings

FittingC2×C13×#137 ⋊ C4
SylowC13 ⋊ C2×#1908

Subgroups

subgroupG/H
centerC22#11719150
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#137C4
socleC22×C13#386
prime radicalC2×#41×D13C22
cosocleC2×C4×D13C24
hypercenterC2×#137#261
hypocenterC13C2×#1908
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1105326);