Finite Group Databasebeta

Dic13×#490 #15870993

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

Aliases

direct productDic13×#490

Splittings

SylowC13 ⋊ C4×#490

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#490C2
socleC23×C13C22×D4
prime radicalC2×C13×#127C22
cosocleC22×C4×C13C24
hypercenterC2×#490D13
hypocenterC13C4×#490
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 177642);