Finite Group Databasebeta

C2×#13116125 #15890783

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

Aliases

direct productC2×#13116125

Splittings

SylowC13 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#88193
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC22×C13×AGL(1,ℤ/8)C2
socleC23×C13#121
hypercenterC22×AGL(1,ℤ/8)D13
hypocenterC13C2×#2051
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 197432);