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C2×AGL(1,𝔽11)×#4296 #49178505

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

Aliases

direct productC2×AGL(1,𝔽11)×#4296
unambiguous semidirect productD11⋊(C2×C5×#4296)
unambiguous semidirect product(C2×D11)⋊(C5×#4296)
unambiguous semidirect product(C11⋊C5)⋊(C22×#4296)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×#4296)
unambiguous semidirect product(C2×D11×#4296)⋊C5

Splittings

Fitting, socleC2×C11×C19 ⋊ C2×C5×C9
derived, HallC11×C19 ⋊ C22×C5×C9
HallC11⋊C5×#4296 ⋊ C22
HallC2×D11×#4296 ⋊ C5
HallC2×C19×AGL(1,𝔽11) ⋊ C9
HallC11×#4296 ⋊ C22×C5
HallC19×C11⋊C5 ⋊ C22×C9
HallC2×C19×D11 ⋊ C5×C9
HallC11⋊C5 ⋊ C22×#4296
HallC2×D11 ⋊ C5×#4296
SylowC19 ⋊ C2×C9×AGL(1,𝔽11)
SylowC11 ⋊ C22×C5×#4296

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽11)×#4296
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC1G
Fitting, socleC2×C11×C19C2×C5×C9
prime radicalC2×C19⋊C3×AGL(1,𝔽11)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

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 214);