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C5×C9×C7⋊AGL(1,𝔽11) #46831464

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

Aliases

direct productC5×C9×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C5×C9×D7)
unambiguous semidirect product(C9×D77)⋊C52
unambiguous semidirect product(C5×C9×D77)⋊C5

Splittings

FittingC5×C7×C9×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C52×C9
HallC5×C7×C9×C11⋊C5 ⋊ C2
HallC5×C9×C11⋊C5 ⋊ D7
HallC5×C7×C11⋊C5 ⋊ C2×C9
HallC9×D77 ⋊ C52
HallC7×C9×C11 ⋊ C2×C52
HallC5×C11⋊C5 ⋊ C9×D7
HallD77 ⋊ C52×C9
HallC9×C11 ⋊ C52×D7
HallC7×C9 ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C52×C9×D7
SylowC7 ⋊ C5×C9×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC5×C9C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C52×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×C7×C11C2×C3×C52
LCSG ▷ C7×C11
UCSC1 ◁ C5×C9

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

1440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 107);