Finite Group Databasebeta

C2×#11927346 #14578385

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

Aliases

direct productC2×#11927346

Splittings

FittingC2×C19×#135 ⋊ C2
SylowC19 ⋊ C2×#576

Subgroups

subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC2×C19×#135C2
socleC22×C19C22×D4
hypercenterC2×#135D19
hypocenterC19C2×#576
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19260);