Finite Group Databasebeta

D19×#367 #14565413

order2432
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD19×#367

Splittings

FittingC19×#367 ⋊ C2
SylowC19 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D19
commutatorC8×C19C22×C4
FrattiniC2×C8C22×D19
FittingC19×#367C2
socleC22×C19C2×D8
prime radicalC22×D19D8
cosocleC2×C8×C19C23
hypercenter#367D19
hypocenterC19C2×#367
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

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, 6288);