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C32×C19⋊AGL(1,𝔽11) #34037865

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

Aliases

direct productC32×C19⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C32×D19)
unambiguous semidirect product(C32×D209)⋊C5

Splittings

Fitting, socle, HallC32×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C32×C5
HallC32×C19×C11⋊C5 ⋊ C2
HallC32×D209 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C32
HallC32×C11⋊C5 ⋊ D19
HallD209 ⋊ C32×C5
HallC32×C19 ⋊ AGL(1,𝔽11)
HallC32×C11 ⋊ C5×D19
HallC11⋊C5 ⋊ C32×D19
SylowC19 ⋊ C32×AGL(1,𝔽11)
SylowC11 ⋊ C32×C5×D19

Subgroups

subgroupG/H
center, hypercenterC32C19⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C19C2×C32×C5
FrattiniC1G
Fitting, socleC32×C11×C19C2×C5
LCSG ▷ C11×C19
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC32×D19×AGL(1,𝔽11), C3×D3×C19⋊AGL(1,𝔽11), C3×D57⋊AGL(1,𝔽11), …
maximal normal subgroup ofC32×D19×AGL(1,𝔽11), C3×D3×C19⋊AGL(1,𝔽11), C3×D57⋊AGL(1,𝔽11), …
maximal quotient ofC32×C19⋊(Dic11⋊C5), C2×C32×C19⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 58);