Finite Group Databasebeta

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C9×D5×C11×D17 #46777890

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

Aliases

direct productC9×D5×C11×D17
unambiguous semidirect product(D5×C17)⋊(C2×C9×C11)
unambiguous semidirect product(C5×D17)⋊(C2×C9×C11)
unambiguous semidirect productD85⋊(C2×C9×C11)

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C22
derived, HallC5×C17 ⋊ C22×C9×C11
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C22×C9
HallC5×C9×C17 ⋊ C22×C11
HallC5×C9×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C9×D5
HallC9×C17 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C9×D17
HallC5×C9 ⋊ C2×C11×D17
SylowC17 ⋊ C2×C9×D5×C11
SylowC5 ⋊ C2×C9×C11×D17

Subgroups

subgroupG/H
center, hypercenterC9×C11D5×D17
commutator, hypocenterC5×C17C22×C9×C11
FrattiniC3C3×D5×C11×D17
FittingC5×C9×C11×C17C22
socleC3×C5×C11×C17C22×C3
prime radicalC3×D5×C11×D17C3
cosocleC3×C5×C17C22×C3×C11
LCSG ▷ C5×C17
UCSC1 ◁ C9×C11

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

3960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 58);