Finite Group Databasebeta

Dic13×#509 #16016239

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productDic13×#509

Splittings

SylowC13 ⋊ C4×#509

Subgroups

subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
Fitting, prime radicalC2×C13×#509C2
socleC22×C13C22×D8
cosocleC2×C8×C13C24
hypercenterC2×#509D13
hypocenterC13C4×#509
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

738 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, 322888);