Finite Group Databasebeta

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C9×D5×C17×D11 #46777893

order33660
automorphism?
homologyAbelianization (H1) = C22×C9×C17 · Schur multiplier (H2) = C2

Aliases

direct productC9×D5×C17×D11
unambiguous semidirect product(D5×C11)⋊(C2×C9×C17)
unambiguous semidirect product(C5×D11)⋊(C2×C9×C17)
unambiguous semidirect productD55⋊(C2×C9×C17)

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C22
derived, HallC5×C11 ⋊ C22×C9×C17
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C22×C9
HallC5×C9×C17 ⋊ C2×D11
HallC5×C9×C11 ⋊ C22×C17
HallC11×C17 ⋊ C2×C9×D5
HallC9×C11 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×C9×D11
HallC5×C9 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C9×D5×C17
SylowC5 ⋊ C2×C9×C17×D11

Subgroups

subgroupG/H
center, hypercenterC9×C17D5×D11
commutator, hypocenterC5×C11C22×C9×C17
FrattiniC3C3×D5×C17×D11
FittingC5×C9×C11×C17C22
socleC3×C5×C11×C17C22×C3
prime radicalC3×D5×C17×D11C3
cosocleC3×C5×C11C22×C3×C17
LCSG ▷ C5×C11
UCSC1 ◁ C9×C17

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

4284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 61);