Finite Group Databasebeta

C2×#137×D19 #14578371

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

Aliases

direct productC2×#137×D19

Splittings

FittingC2×C19×#137 ⋊ C2
SylowC19 ⋊ C22×#137

Subgroups

subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC2×C19×#137C2
socleC22×C19C22×D4
prime radicalC2×#41×D19C2
hypercenterC2×#137D19
hypocenterC19C22×#137
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

1464 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, 19246);