Finite Group Databasebeta

C2×#13116788 #16016810

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116788

Splittings

FittingC2×C13×#360 ⋊ C2
SylowC13 ⋊ C2×#2191

Subgroups

subgroupG/H
centerC22#11718434
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#360C2
socleC22×C13#447
prime radicalC2×#11719473C2
hypercenterC2×#360D13
hypocenterC13C2×#2191
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

1128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323459);