Finite Group Databasebeta

Dic13×#365 #15778305

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productDic13×#365

Splittings

SylowC13 ⋊ C4×#365

Subgroups

subgroupG/H
centerC22D13×#106
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C13×#365C2
socleC22×C13C2×#106
prime radicalC23×C13C2×SD16
cosocleC22×C8×C13C23
hypercenterC2×#365D13
hypocenterC13C4×#365
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84954);