Finite Group Databasebeta

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C19×C25⋊(D13⋊C3) #49150216

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C25⋊(D13⋊C3)
unambiguous semidirect productC25⋊(C19×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C19×D25)
unambiguous semidirect productD325⋊(C3×C19)

Splittings

Fitting, HallC13×C19×C25 ⋊ C2×C3
derived, HallC13×C25 ⋊ C2×C3×C19
HallC19×C25×C13⋊C3 ⋊ C2
HallC19×D325 ⋊ C3
HallC25×C13⋊C3 ⋊ C2×C19
HallC19×C13⋊C3 ⋊ D25
HallD325 ⋊ C3×C19
HallC19×C25 ⋊ D13⋊C3
HallC13×C19 ⋊ C3×D25
HallC13⋊C3 ⋊ C19×D25
SylowC25 ⋊ C19×D13⋊C3
SylowC13 ⋊ C3×C19×D25

Subgroups

subgroupG/H
center, hypercenterC19C25⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C25C2×C3×C19
FrattiniC5C19×C5⋊(D13⋊C3)
FittingC13×C19×C25C2×C3
socleC5×C13×C19C3×D5
LCSG ▷ C13×C25
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

1748 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 42);