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C3⋊((C11⋊C5)⋊(D19⋊C3)) #34037852

order18810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊(D19⋊C3))
unambiguous semidirect product(C11⋊C5)⋊(C3⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C3⋊(C11⋊(D19⋊C3)))⋊C5
unambiguous semidirect product(C3⋊(C19⋊AGL(1,𝔽11)))⋊C3

Splittings

Fitting, socle, derivedC3×C11×C19 ⋊ C2×C3×C5
HallC3×C11⋊C5×C19⋊C3 ⋊ C2
HallC3⋊(C11⋊(D19⋊C3)) ⋊ C5
HallC3×C11×C19⋊C3 ⋊ C2×C5
HallC19×C11⋊C5 ⋊ C3×D3
HallC11×C19 ⋊ C3×C5×D3
HallC3×C19⋊C3 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ C3×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×C3⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C19C2×C3×C5
LCSG ▷ C3×C11×C19
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 627

Polycyclic presentation:

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

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×C3⋊AGL(1,𝔽11), AGL(1,𝔽11)×C3⋊(D19⋊C3), D3×(C11⋊C5)⋊(D19⋊C3), …
maximal normal subgroup ofD19⋊C3×C3⋊AGL(1,𝔽11), AGL(1,𝔽11)×C3⋊(D19⋊C3), D3×(C11⋊C5)⋊(D19⋊C3), …
maximal quotient ofC3⋊((C11⋊C5)⋊((C19⋊C3)⋊C4)), C2×C3⋊((C11⋊C5)⋊(D19⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 45);