Finite Group Databasebeta

← Prev (#44535451) Next (#44535453) →

C19×C3⋊(D11⋊C25) #44535452

order31350
automorphism?
homologyAbelianization (H1) = C2×C19×C25 · Schur multiplier (H2) = C1

Aliases

direct productC19×C3⋊(D11⋊C25)
unambiguous semidirect productC3⋊(C19×D11⋊C25)
unambiguous semidirect productD33⋊(C19×C25)
unambiguous semidirect product(C11⋊C25)⋊(D3×C19)
unambiguous semidirect product(C19×D33)⋊C25

Splittings

derived, HallC3×C11 ⋊ C2×C19×C25
HallC3×C19×C11⋊C25 ⋊ C2
HallC19×C11⋊C25 ⋊ D3
HallC19×D33 ⋊ C25
HallC3×C11⋊C25 ⋊ C2×C19
HallC3×C11×C19 ⋊ C2×C25
HallC11⋊C25 ⋊ D3×C19
HallC11×C19 ⋊ D3×C25
HallD33 ⋊ C19×C25
HallC3×C19 ⋊ D11⋊C25
SylowC11 ⋊ D3×C19×C25
SylowC3 ⋊ C19×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC5×C19C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C2×C19×C25
FrattiniC5C19×C3⋊AGL(1,𝔽11)
Fitting, socleC3×C5×C11×C19C2×C5
prime radicalC5×C19×D33C5
cosocleC3×C5×C11C2×C5×C19
LCSG ▷ C3×C11
UCSC1 ◁ C5×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

1710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 25);