Finite Group Databasebeta

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C2×AGL(1,𝔽11)×#4294 #49178331

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

Aliases

direct productC2×AGL(1,𝔽11)×#4294
unambiguous semidirect productD11⋊(C2×C5×#4294)
unambiguous semidirect product(C2×D11)⋊(C5×#4294)
unambiguous semidirect product(C11⋊C5)⋊(C22×#4294)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×#4294)
unambiguous semidirect product(C2×D11×#4294)⋊C5

Splittings

derived, HallC11×C19 ⋊ C22×C5×C9
HallC11⋊C5×#4294 ⋊ C22
HallC2×D11×#4294 ⋊ C5
HallC2×C19×AGL(1,𝔽11) ⋊ C9
HallC11×#4294 ⋊ C22×C5
HallC19×C11⋊C5 ⋊ C22×C9
HallC2×C19×D11 ⋊ C5×C9
HallC11⋊C5 ⋊ C22×#4294
HallC2×D11 ⋊ C5×#4294
SylowC19 ⋊ C2×C9×AGL(1,𝔽11)
SylowC11 ⋊ C22×C5×#4294

Subgroups

subgroupG/H
center, hypercenterC2×C3C19⋊C3×AGL(1,𝔽11)
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC3C2×C19⋊C3×AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C19C2×C3×C5
prime radicalC2×C3×C19×AGL(1,𝔽11)C3
cosocleC3×C11×C19C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3762

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 40);