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C3×(C11⋊C5)⋊(D19⋊C3) #34037849

order18810
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct 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(C11⋊(D19⋊C3))⋊(C3×C5)
unambiguous semidirect product(C19⋊AGL(1,𝔽11))⋊C32
unambiguous semidirect product(C3×C11⋊(D19⋊C3))⋊C5
unambiguous semidirect product(C3×C19⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC3×C11×C19 ⋊ C2×C3×C5
derived, HallC11×C19 ⋊ C2×C32×C5
HallC3×C11⋊C5×C19⋊C3 ⋊ C2
HallC3×C11⋊(D19⋊C3) ⋊ C5
HallC19⋊AGL(1,𝔽11) ⋊ C32
HallC3×C11×C19⋊C3 ⋊ C2×C5
HallC19×C11⋊C5 ⋊ C2×C32
HallD209 ⋊ C32×C5
HallC3×C19⋊C3 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D19⋊C3
SylowC19 ⋊ C32×AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊(D19⋊C3)
commutator, cosocle, hypocenterC11×C19C2×C32×C5
FrattiniC1G
Fitting, socleC3×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 627

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽11)×D19⋊C3, D3×(C11⋊C5)⋊(D19⋊C3), (C3⋊AGL(1,𝔽11))⋊(D19⋊C3), …
maximal normal subgroup ofC3×AGL(1,𝔽11)×D19⋊C3, D3×(C11⋊C5)⋊(D19⋊C3), (C3⋊AGL(1,𝔽11))⋊(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, 42);