Finite Group Databasebeta

C2×#13130981 #16799178

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13130981
unambiguous semidirect productD13⋊#1968

Splittings

FittingC22×C13×SD16 ⋊ C4
SylowC13 ⋊ C2×#1968

Subgroups

subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC22×C13×SD16C4
socleC23×C13C4×D4
prime radicalC22×D4×D13C22
cosocleC2×C4×D13C24
hypercenterC22×SD16#261
hypocenterC13C2×#1968
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1105827);