Finite Group Databasebeta

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C2×C5×C9×C11×D17 #46777952

order33660
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×C11×D17
unambiguous semidirect productC17⋊(C22×C5×C9×C11)
unambiguous semidirect product(C2×C17)⋊(C2×C5×C9×C11)

Splittings

FittingC2×C5×C9×C11×C17 ⋊ C2
derived, SylowC17 ⋊ C22×C5×C9×C11
HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C22×C5
HallC5×C11×C17 ⋊ C22×C9
HallC5×C9×C17 ⋊ C22×C11
HallC11×C17 ⋊ C22×C5×C9
HallC9×C17 ⋊ C22×C5×C11
HallC5×C17 ⋊ C22×C9×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9×C11D17
commutator, hypocenterC17C22×C5×C9×C11
FrattiniC3C2×C3×C5×C11×D17
FittingC2×C5×C9×C11×C17C2
socleC2×C3×C5×C11×C17C2×C3
prime radicalC2×C3×C5×C11×D17C3
cosocleC3×C17C22×C3×C5×C11
LCSG ▷ C17
UCSC1 ◁ C2×C5×C9×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

9900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 120);