Finite Group Databasebeta

C2×#13123351 #16726457

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13123351

Splittings

FittingC2×C13×#416 ⋊ C2
SylowC13 ⋊ C2×#2896

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#416C2
socleC23×C13C22×D4
prime radicalC22×#41×D13C2
cosocleC2×C4×C13C25
hypercenterC2×#416D13
hypocenterC13C2×#2896
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

5198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033106);