Finite Group Databasebeta

Dic13×#455 #15868805

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productDic13×#455

Splittings

SylowC13 ⋊ C4×#455

Subgroups

subgroupG/H
centerC22D13×#120
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#455C2
socleC22×C13C2×#120
prime radicalC2×C13×H(5,𝔽2)C22
cosocleC22×C4×C13C24
hypercenterC2×#455D13
hypocenterC13C4×#455
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

1442 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, 175454);