Finite Group Databasebeta

← Prev (#44535462) Next (#44535464) →

(C19⋊C3)⋊(D11⋊C25) #44535463

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C19⋊C3)⋊(D11⋊C25)
unambiguous semidirect product(C11⋊C25)⋊(D19⋊C3)
unambiguous semidirect product(C11⋊(D19⋊C3))⋊C25
unambiguous semidirect product(C19⋊(D11⋊C25))⋊C3

Splittings

derived, HallC11×C19 ⋊ C2×C3×C25
HallC19⋊C3×C11⋊C25 ⋊ C2
HallC19⋊(D11⋊C25) ⋊ C3
HallC19×C11⋊C25 ⋊ C2×C3
HallC11⋊(D19⋊C3) ⋊ C25
HallC11×C19⋊C3 ⋊ C2×C25
HallD209 ⋊ C3×C25
HallC11⋊C25 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D11⋊C25
SylowC19 ⋊ C3×D11⋊C25
SylowC11 ⋊ C25×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC5(C11⋊C5)⋊(D19⋊C3)
commutator, hypocenterC11×C19C2×C3×C25
Fitting, socle, cosocleC5×C11×C19C2×C3×C5
prime radicalC5×C11⋊(D19⋊C3)C5
LCSG ▷ C11×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Polycyclic presentation:

2,3,5,11,19,5|c^5=f,d^a=d^10,e^a=e^18,e^b=e^7,d^c=d^4

Conjugacy classes & character table

270 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 36);