Finite Group Databasebeta

C2×#11927340 #14578378

order2432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#11927340

Splittings

FittingC2×C19×AGL(1,ℤ/8) ⋊ C2
SylowC19 ⋊ C2×#575

Subgroups

subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC2×C19×AGL(1,ℤ/8)C2
socleC22×C19C22×D4
hypercenterC2×AGL(1,ℤ/8)D19
hypocenterC19C2×#575
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19253);