Finite Group Databasebeta

C2×#13130841 #16798571

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

Aliases

direct productC2×#13130841
unambiguous semidirect productD13⋊#1885

Splittings

FittingC2×C13×#124 ⋊ C4
SylowC13 ⋊ C2×#1885

Subgroups

subgroupG/H
centerC22#11719150
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#124C4
socleC22×C13#386
prime radicalC22×D4×D13C22
cosocleC2×C4×D13C24
hypercenterC2×#124#261
hypocenterC13C2×#1885
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

1966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1105220);