Finite Group Databasebeta

C2×#11926459 #14566839

order2432
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#11926459

Splittings

FittingC22×C22⋊C4×C19 ⋊ C2
SylowC19 ⋊ C2×#394

Subgroups

subgroupG/H
centerC24C22×D19
commutator, cosocleC23×C19C24
FrattiniC23C23×D19
FittingC22×C22⋊C4×C19C2
socleC24×C19C23
prime radicalC23×C22⋊D19C2
hypercenterC22×C22⋊C4D19
hypocenterC19C2×#394
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7714);