Finite Group Databasebeta

C2×#13130676 #16797790

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13130676
unambiguous semidirect productD13⋊#1788

Splittings

FittingC22×C13×#41 ⋊ C4
SylowC13 ⋊ C2×#1788

Subgroups

subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC22×C13×#41C4
socleC23×C13C2×C22⋊C4
prime radicalC22×#41×D13C2
cosocleC2×C4×D13C24
hypercenterC22×#41#261
hypocenterC13C2×#1788
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

4070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1104439);