Finite Group Databasebeta

C2×D13×B(4,𝔽2) #16729630

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC2×D13×B(4,𝔽2)

Splittings

FittingC2×C13×B(4,𝔽2) ⋊ C2
SylowC13 ⋊ C22×B(4,𝔽2)

Subgroups

subgroupG/H
centerC22D13×#120
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×B(4,𝔽2)C2
socleC22×C13C2×#120
hypercenterC2×B(4,𝔽2)D13
hypocenterC13C22×B(4,𝔽2)
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C2×B(4,𝔽2)

7014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 1036279);