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C2×C17×C9⋊AGL(1,𝔽11) #46777873

order33660
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×C9⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C9)⋊(C17×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C17×D9)
unambiguous semidirect product(C2×D99)⋊(C5×C17)
unambiguous semidirect product(C2×C17×D99)⋊C5

Splittings

FittingC2×C9×C11×C17 ⋊ C2×C5
derived, HallC9×C11 ⋊ C22×C5×C17
HallC9×C17×C11⋊C5 ⋊ C22
HallC2×C17×D99 ⋊ C5
HallC9×C11×C17 ⋊ C22×C5
HallC17×C11⋊C5 ⋊ C2×D9
HallC9×C11⋊C5 ⋊ C22×C17
HallC2×D99 ⋊ C5×C17
HallC11×C17 ⋊ C2×C5×D9
HallC9×C17 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C17×D9
SylowC11 ⋊ C2×C5×C17×D9
SylowC9 ⋊ C2×C17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C17C9⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC9×C11C22×C5×C17
FrattiniC3C2×C17×C3⋊AGL(1,𝔽11)
FittingC2×C9×C11×C17C2×C5
socleC2×C3×C11×C17C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C2×C17

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3366

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 41);