Finite Group Databasebeta

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C3×C5×C19×AGL(1,𝔽11) #44535473

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C19 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C19×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C52×C19)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C5×C19)
unambiguous semidirect product(C3×D11)⋊(C52×C19)
unambiguous semidirect product(C5×D11)⋊(C3×C5×C19)
unambiguous semidirect product(C3×C5×D11)⋊(C5×C19)
unambiguous semidirect product(C3×C19×D11)⋊C52
unambiguous semidirect product(C3×C5×C19×D11)⋊C5

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C52×C19
HallC3×C5×C19×C11⋊C5 ⋊ C2
HallC5×C19×C11⋊C5 ⋊ C2×C3
HallC3×C19×D11 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ C2×C19
HallC3×C11×C19 ⋊ C2×C52
HallC19×D11 ⋊ C3×C52
HallC5×C11⋊C5 ⋊ C2×C3×C19
HallC11×C19 ⋊ C2×C3×C52
HallC3×D11 ⋊ C52×C19
HallC3×C11 ⋊ C2×C52×C19
HallD11 ⋊ C3×C52×C19

Subgroups

subgroupG/H
center, hypercenterC3×C5×C19AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C52×C19
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C5×C19

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

3135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 46);