Finite Group Databasebeta

Dic13×#471 #15869785

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

Aliases

direct productDic13×#471

Splittings

SylowC13 ⋊ C4×#471

Subgroups

subgroupG/H
centerC22D13×#121
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#471C2
socleC22×C13C2×#121
prime radicalC2×C13×AGL(1,ℤ/8)C22
cosocleC22×C4×C13C24
hypercenterC2×#471D13
hypocenterC13C4×#471
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#471

914 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, 176434);