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C5⋊((C11⋊C5)⋊(D19⋊C3)) #44535468

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊((C11⋊C5)⋊(D19⋊C3))
unambiguous semidirect product(C11⋊C5)⋊(C5⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect product(C5⋊(C11⋊(D19⋊C3)))⋊C5
unambiguous semidirect product(C5⋊(C19⋊AGL(1,𝔽11)))⋊C3

Splittings

Fitting, socle, derivedC5×C11×C19 ⋊ C2×C3×C5
HallC5×C11⋊C5×C19⋊C3 ⋊ C2
HallC5⋊(C19⋊AGL(1,𝔽11)) ⋊ C3
HallC5×C19×C11⋊C5 ⋊ C2×C3
HallC11×C19⋊C3 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ D19⋊C3
HallC11×C19 ⋊ C3×C5×D5
HallC19⋊C3 ⋊ C5⋊AGL(1,𝔽11)
SylowC19 ⋊ C3×C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×C5⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C19C2×C3×C5
LCSG ▷ C5×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Polycyclic presentation:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 41);