Finite Group Databasebeta

C2×#13115214 #15864419

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115214

Splittings

SylowC13 ⋊ C2×#1883

Subgroups

subgroupG/H
centerC23#88191
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC22×C13×AGL(1,ℤ/8)C2
socleC23×C13#120
cosocleC22×C4×C13C24
hypercenterC22×AGL(1,ℤ/8)D13
hypocenterC13C2×#1883
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171068);