Finite Group Databasebeta

C2×#13116007 #15890342

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116007

Splittings

FittingC2×C13×H(3,ℤ/4) ⋊ C2
SylowC13 ⋊ C2×#2031

Subgroups

subgroupG/H
centerC2×C4#88129
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC22×C13#393
prime radicalC22×#6127C22
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13C2×#2031
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

316 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 196991);