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C2×C9×C17⋊AGL(1,𝔽11) #46777871

order33660
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C17⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C17)⋊(C9×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C9×D17)
unambiguous semidirect product(C2×D187)⋊(C5×C9)
unambiguous semidirect product(C2×C9×D187)⋊C5

Splittings

FittingC2×C9×C11×C17 ⋊ C2×C5
derived, HallC11×C17 ⋊ C22×C5×C9
HallC9×C17×C11⋊C5 ⋊ C22
HallC2×C9×D187 ⋊ C5
HallC9×C11×C17 ⋊ C22×C5
HallC17×C11⋊C5 ⋊ C22×C9
HallC2×D187 ⋊ C5×C9
HallC9×C11⋊C5 ⋊ C2×D17
HallC9×C17 ⋊ C2×AGL(1,𝔽11)
HallC9×C11 ⋊ C2×C5×D17
HallC11⋊C5 ⋊ C2×C9×D17
SylowC17 ⋊ C2×C9×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C9×D17

Subgroups

subgroupG/H
center, hypercenterC2×C9C17⋊AGL(1,𝔽11)
commutator, hypocenterC11×C17C22×C5×C9
FrattiniC3C2×C3×C17⋊AGL(1,𝔽11)
FittingC2×C9×C11×C17C2×C5
socleC2×C3×C11×C17C2×C3×C5
prime radicalC2×C3×C17⋊AGL(1,𝔽11)C3
cosocleC3×C11×C17C22×C3×C5
LCSG ▷ C11×C17
UCSC1 ◁ C2×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3366

Conjugacy classes & character table

1206 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 39);