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C19×C3⋊(C3⋊AGL(1,𝔽11)) #34037871

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C3

Aliases

direct productC19×C3⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C19×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3⋊D3×C19)
unambiguous semidirect product(C3⋊D33)⋊(C5×C19)
unambiguous semidirect product(C19×C3⋊D33)⋊C5

Splittings

Fitting, socle, HallC32×C11×C19 ⋊ C2×C5
derived, HallC32×C11 ⋊ C2×C5×C19
HallC32×C19×C11⋊C5 ⋊ C2
HallC19×C3⋊D33 ⋊ C5
HallC19×C11⋊C5 ⋊ C3⋊D3
HallC32×C11⋊C5 ⋊ C2×C19
HallC11×C19 ⋊ C5×C3⋊D3
HallC3⋊D33 ⋊ C5×C19
HallC32×C19 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3⋊D3×C19
SylowC11 ⋊ C5×C3⋊D3×C19
SylowC32 ⋊ C19×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C3⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC32×C11C2×C5×C19
FrattiniC1G
Fitting, socleC32×C11×C19C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

741 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C19×C3⋊AGL(1,𝔽11), D57⋊(C3⋊AGL(1,𝔽11)), D19×C3⋊(C3⋊AGL(1,𝔽11)), …
maximal normal subgroup ofD3×C19×C3⋊AGL(1,𝔽11), D57⋊(C3⋊AGL(1,𝔽11)), D19×C3⋊(C3⋊AGL(1,𝔽11)), …
maximal quotient ofC19×C3⋊(C3⋊(Dic11⋊C5)), C2×C19×C3⋊(C3⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 64);