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C11×C5⋊AGL(1,𝔽19) #34037859

order18810
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊AGL(1,𝔽19)
unambiguous semidirect productC5⋊(C11×AGL(1,𝔽19))
unambiguous semidirect product#4296⋊(D5×C11)

Splittings

Fitting, socle, HallC5×C11×C19 ⋊ C2×C9
derived, HallC5×C19 ⋊ C2×C9×C11
HallC5×C11×#4296 ⋊ C2
HallC11×D95 ⋊ C9
HallC11×#4296 ⋊ D5
HallC5×#4296 ⋊ C2×C11
HallC11×C19 ⋊ C9×D5
HallD95 ⋊ C9×C11
Hall#4296 ⋊ D5×C11
HallC5×C11 ⋊ AGL(1,𝔽19)
SylowC19 ⋊ C9×D5×C11
SylowC5 ⋊ C11×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC11C5⋊AGL(1,𝔽19)
commutator, hypocenterC5×C19C2×C9×C11
FrattiniC1G
Fitting, socleC5×C11×C19C2×C9
prime radicalC11×C5⋊(D19⋊C3)C3
cosocleC5×C19⋊C3C2×C3×C11
LCSG ▷ C5×C19
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×C11×AGL(1,𝔽19), D11×C5⋊AGL(1,𝔽19), D55⋊AGL(1,𝔽19), …
maximal normal subgroup ofD5×C11×AGL(1,𝔽19), D11×C5⋊AGL(1,𝔽19), D55⋊AGL(1,𝔽19), …
maximal quotient ofC11×#4296⋊Dic5, C2×C11×C5⋊AGL(1,𝔽19)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 52);