Finite Group Databasebeta

Dic13×#357 #15778125

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productDic13×#357

Splittings

SylowC13 ⋊ C4×#357

Subgroups

subgroupG/H
centerC23D8×D13
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C13×#357C2
socleC23×C13C2×D8
prime radicalC22×C13×D8C22
cosocleC22×C8×C13C23
hypercenterC2×#357D13
hypocenterC13C4×#357
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

534 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, 84774);