Finite Group Databasebeta

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C19×D825 #44535445

order31350
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D825
unambiguous semidirect productC3⋊(C19×D275)
unambiguous semidirect productC11⋊(C19×D75)
unambiguous semidirect productC25⋊(C19×D33)

Splittings

Fitting, HallC3×C11×C19×C25 ⋊ C2
derived, HallC3×C11×C25 ⋊ C2×C19
HallC11×C19×C25 ⋊ D3
HallC3×C19×C25 ⋊ D11
HallC3×C11×C19 ⋊ D25
HallC19×C25 ⋊ D33
HallC11×C25 ⋊ D3×C19
HallC11×C19 ⋊ D75
HallC3×C25 ⋊ C19×D11
HallC3×C19 ⋊ D275
HallC3×C11 ⋊ C19×D25
SylowC25 ⋊ C19×D33
SylowC11 ⋊ C19×D75
SylowC3 ⋊ C19×D275

Subgroups

subgroupG/H
center, hypercenterC19D825
commutator, cosocle, hypocenterC3×C11×C25C2×C19
FrattiniC5C19×D165
FittingC3×C11×C19×C25C2
socleC3×C5×C11×C19D5
LCSG ▷ C3×C11×C25
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

7866 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 18);