Finite Group Databasebeta

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C2×C5×C11×C17×D9 #46777945

order33660
automorphism?
homologyAbelianization (H1) = C22×C5×C11×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×C17×D9
unambiguous semidirect productC9⋊(C22×C5×C11×C17)
unambiguous semidirect product(C2×C9)⋊(C2×C5×C11×C17)

Splittings

FittingC2×C5×C9×C11×C17 ⋊ C2
derived, SylowC9 ⋊ C22×C5×C11×C17
HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C22×C5
HallC5×C9×C17 ⋊ C22×C11
HallC5×C9×C11 ⋊ C22×C17
HallC9×C17 ⋊ C22×C5×C11
HallC9×C11 ⋊ C22×C5×C17
HallC5×C9 ⋊ C22×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C17D9
commutator, cosocle, hypocenterC9C22×C5×C11×C17
FrattiniC3C2×C5×D3×C11×C17
FittingC2×C5×C9×C11×C17C2
socleC2×C3×C5×C11×C17D3
LCSG ▷ C9
UCSC1 ◁ C2×C5×C11×C17

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

11220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 113);