Finite Group Databasebeta

C2×#11926466 #14566855

order2432
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11926466

Splittings

FittingC22×C4⋊C4×C19 ⋊ C2
SylowC19 ⋊ C2×#396

Subgroups

subgroupG/H
centerC24C22×D19
commutator, cosocleC23×C19C24
FrattiniC23C23×D19
FittingC22×C4⋊C4×C19C2
socleC24×C19C23
prime radicalC24×D19C22
hypercenterC22×C4⋊C4D19
hypocenterC19C2×#396
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C4⋊C4

908 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, 7730);