Finite Group Databasebeta

Dic13×#508 #16016202

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

Aliases

direct productDic13×#508

Splittings

SylowC13 ⋊ C4×#508

Subgroups

subgroupG/H
centerC2×C4D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
Fitting, prime radicalC2×C13×#508C2
socleC22×C13C22×D8
cosocleC2×C8×C13C24
hypercenterC2×#508D13
hypocenterC13C4×#508
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322851);