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C2×C3×C29×AGL(1,𝔽11) #34062345

order19140
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C29×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C3×C5×C29)
unambiguous semidirect product(C2×D11)⋊(C3×C5×C29)
unambiguous semidirect product(C11⋊C5)⋊(C22×C3×C29)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C3×C29)
unambiguous semidirect product(C2×C3×D11)⋊(C5×C29)
unambiguous semidirect product(C2×D11×C29)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D11×C29)⋊C5

Splittings

Fitting, socleC2×C3×C11×C29 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C3×C5×C29
HallC3×C29×C11⋊C5 ⋊ C22
HallC2×C3×D11×C29 ⋊ C5
HallC29×C11⋊C5 ⋊ C22×C3
HallC2×D11×C29 ⋊ C3×C5
HallC3×C11×C29 ⋊ C22×C5
HallC11×C29 ⋊ C22×C3×C5
HallC3×C11⋊C5 ⋊ C22×C29
HallC2×C3×D11 ⋊ C5×C29
HallC11⋊C5 ⋊ C22×C3×C29
HallC2×D11 ⋊ C3×C5×C29
HallC3×C11 ⋊ C22×C5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C5×C29
FrattiniC1G
Fitting, socleC2×C3×C11×C29C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1914

Conjugacy classes & character table

1914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 38);