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C3⋊(C5⋊(C11⋊(D19⋊C3))) #34037889

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

Aliases

unambiguous semidirect productC3⋊(C5⋊(C11⋊(D19⋊C3)))
unambiguous semidirect productC5⋊(C3⋊(C11⋊(D19⋊C3)))
unambiguous semidirect productC11⋊(C3⋊(C5⋊(D19⋊C3)))
unambiguous semidirect product(C19⋊C3)⋊D165
unambiguous semidirect productD3135⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C19 ⋊ C2×C3
HallC3×C5×C11×C19⋊C3 ⋊ C2
HallC3×C11×C19⋊C3 ⋊ D5
HallC5×C11×C19 ⋊ C3×D3
HallC3×C5×C19⋊C3 ⋊ D11
HallC11×C19 ⋊ C3×D15
HallC3×C19⋊C3 ⋊ D55
HallC5×C19 ⋊ C3×D33
HallC5×C11 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ C3×D165
SylowC11 ⋊ C3⋊(C5⋊(D19⋊C3))
SylowC5 ⋊ C3⋊(C11⋊(D19⋊C3))

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Polycyclic presentation:

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

Conjugacy classes & character table

747 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×D165, D11×C3⋊(C5⋊(D19⋊C3)), D15×C11⋊(D19⋊C3), …
maximal normal subgroup ofD19⋊C3×D165, D11×C3⋊(C5⋊(D19⋊C3)), D15×C11⋊(D19⋊C3), …
maximal quotient ofC3⋊(C11⋊((C19⋊C3)⋊Dic5)), C2×C3⋊(C5⋊(C11⋊(D19⋊C3)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 82);