Finite Group Databasebeta

D19×#391 #14566101

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productD19×#391

Splittings

FittingC19×#391 ⋊ C2
SylowC19 ⋊ C2×#391

Subgroups

subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC19×#391C2
socle, cosocleC23×C19C24
prime radicalC23×D19C23
hypercenter#391D19
hypocenterC19C2×#391
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD19×#1272, #18070535, #18070626, …
maximal normal subgroup ofD19×#1272, #18070535, #18070626, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6976);