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(C11⋊C5)⋊AGL(1,𝔽19) #34037845

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊AGL(1,𝔽19)
unambiguous semidirect product#4296⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊AGL(1,𝔽19))⋊C5

Splittings

Fitting, socle, derived, HallC11×C19 ⋊ C2×C5×C9
HallC11⋊C5×#4296 ⋊ C2
HallC11⋊AGL(1,𝔽19) ⋊ C5
HallC19⋊AGL(1,𝔽11) ⋊ C9
HallC11×#4296 ⋊ C2×C5
HallC19×C11⋊C5 ⋊ C2×C9
HallD209 ⋊ C5×C9
Hall#4296 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ AGL(1,𝔽19)
SylowC19 ⋊ C9×AGL(1,𝔽11)
SylowC11 ⋊ C5×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C19C2×C5×C9
prime radical(C11⋊C5)⋊(D19⋊C3)C3
cosocleC11×C19⋊C3C2×C3×C5
LCSG ▷ C11×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 209

Polycyclic presentation:

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

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×AGL(1,𝔽19), C2×(C11⋊C5)⋊AGL(1,𝔽19)
maximal normal subgroup ofAGL(1,𝔽11)×AGL(1,𝔽19), C2×(C11⋊C5)⋊AGL(1,𝔽19)
maximal quotient of(C11⋊C5)⋊(#4296⋊C4), C2×(C11⋊C5)⋊AGL(1,𝔽19)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 38);