Finite Group Databasebeta

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C5×C7×C9×AGL(1,𝔽11) #46831463

order34650
automorphism?
homologyAbelianization (H1) = C2×C52×C7×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×C9×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C52×C7×C9)
unambiguous semidirect product(C11⋊C5)⋊(C2×C5×C7×C9)
unambiguous semidirect product(C5×D11)⋊(C5×C7×C9)
unambiguous semidirect product(C9×D11)⋊(C52×C7)
unambiguous semidirect product(C5×C9×D11)⋊(C5×C7)
unambiguous semidirect product(C7×C9×D11)⋊C52
unambiguous semidirect product(C5×C7×C9×D11)⋊C5

Splittings

FittingC5×C7×C9×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C52×C7×C9
HallC5×C7×C9×C11⋊C5 ⋊ C2
HallC5×C9×C11⋊C5 ⋊ C2×C7
HallC5×C7×C11⋊C5 ⋊ C2×C9
HallC7×C9×D11 ⋊ C52
HallC7×C9×C11 ⋊ C2×C52
HallC5×C11⋊C5 ⋊ C2×C7×C9
HallC9×D11 ⋊ C52×C7
HallC7×D11 ⋊ C52×C9
HallC9×C11 ⋊ C2×C52×C7
HallC7×C11 ⋊ C2×C52×C9
HallD11 ⋊ C52×C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C7×C9AGL(1,𝔽11)
commutator, hypocenterC11C2×C52×C7×C9
FrattiniC3C3×C5×C7×AGL(1,𝔽11)
FittingC5×C7×C9×C11C2×C5
socleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C5×C7×AGL(1,𝔽11)C3
cosocleC3×C11C2×C3×C52×C7
LCSG ▷ C11
UCSC1 ◁ C5×C7×C9

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 106);