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C5×(C11⋊C5)⋊(D7⋊C9) #46831455

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

Aliases

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

Splittings

derived, HallC7×C11 ⋊ C2×C52×C9
HallC5×C11⋊C5×C7⋊C9 ⋊ C2
HallC5×C7⋊AGL(1,𝔽11) ⋊ C9
HallC5×C7×C11⋊C5 ⋊ C2×C9
HallC11⋊(D7⋊C9) ⋊ C52
HallC11×C7⋊C9 ⋊ C2×C52
HallC5×C11⋊C5 ⋊ D7⋊C9
HallD77 ⋊ C52×C9
HallC7⋊C9 ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C52×D7⋊C9
SylowC7 ⋊ C5×C9×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C52×C9
FrattiniC3C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11)
Fitting, socleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C5×C7⋊AGL(1,𝔽11)C3
cosocleC3×C7×C11C2×C3×C52
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 98);