Finite Group Databasebeta

C2×#13117052 #16017805

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

Aliases

direct productC2×#13117052

Splittings

FittingC2×C13×#365 ⋊ C2
SylowC13 ⋊ C2×#2238

Subgroups

subgroupG/H
centerC22#11718524
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#365C2
socleC22×C13#481
prime radicalC2×#11718526C2
hypercenterC2×#365D13
hypocenterC13C2×#2238
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 324454);