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C2×(C11⋊C5)⋊AGL(1,𝔽19) #49178504

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C11⋊C5)⋊AGL(1,𝔽19)
unambiguous semidirect product(C2×C11⋊C5)⋊AGL(1,𝔽19)
unambiguous semidirect product(C2×#4296)⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊AGL(1,𝔽19))⋊C5

Splittings

Fitting, socleC2×C11×C19 ⋊ C2×C5×C9
derived, HallC11×C19 ⋊ C22×C5×C9
HallC11⋊C5×#4296 ⋊ C22
HallC2×C11⋊AGL(1,𝔽19) ⋊ C5
HallC2×C19⋊AGL(1,𝔽11) ⋊ C9
HallC11×#4296 ⋊ C22×C5
HallC19×C11⋊C5 ⋊ C22×C9
HallC2×D209 ⋊ C5×C9
Hall#4296 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×AGL(1,𝔽19)
SylowC19 ⋊ C2×C9×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC2(C11⋊C5)⋊AGL(1,𝔽19)
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC1G
Fitting, socleC2×C11×C19C2×C5×C9
prime radicalC2×(C11⋊C5)⋊(D19⋊C3)C3
cosocleC11×C19⋊C3C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 418

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 213);