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C5×C11⋊AGL(1,𝔽19) #34037857

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

Aliases

direct productC5×C11⋊AGL(1,𝔽19)
unambiguous semidirect product#4296⋊(C5×D11)

Splittings

Fitting, socle, HallC5×C11×C19 ⋊ C2×C9
derived, HallC11×C19 ⋊ C2×C5×C9
HallC5×C11×#4296 ⋊ C2
HallC5×D209 ⋊ C9
HallC11×#4296 ⋊ C2×C5
HallC5×#4296 ⋊ D11
HallD209 ⋊ C5×C9
Hall#4296 ⋊ C5×D11
HallC5×C19 ⋊ C9×D11
HallC5×C11 ⋊ AGL(1,𝔽19)
SylowC19 ⋊ C5×C9×D11
SylowC11 ⋊ C5×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC5C11⋊AGL(1,𝔽19)
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC1G
Fitting, socleC5×C11×C19C2×C9
prime radicalC5×C11⋊(D19⋊C3)C3
cosocleC11×C19⋊C3C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×AGL(1,𝔽19), D5×C11⋊AGL(1,𝔽19), D55⋊AGL(1,𝔽19), …
maximal normal subgroup ofC5×D11×AGL(1,𝔽19), D5×C11⋊AGL(1,𝔽19), D55⋊AGL(1,𝔽19), …
maximal quotient ofC5×C11⋊(#4296⋊C4), C2×C5×C11⋊AGL(1,𝔽19)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 50);