Finite Group Databasebeta

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C17×D9×D55 #46777929

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

Aliases

direct productC17×D9×D55
unambiguous semidirect product(C5×D9)⋊(C17×D11)
unambiguous semidirect product(C11×D9)⋊(D5×C17)

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C22
derived, HallC5×C9×C11 ⋊ C22×C17
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C17 ⋊ C2×D11
HallC11×C17 ⋊ D5×D9
HallC9×C17 ⋊ C2×D55
HallC9×C11 ⋊ C2×D5×C17
HallC5×C17 ⋊ D9×D11
HallC5×C11 ⋊ C2×C17×D9
HallC5×C9 ⋊ C2×C17×D11
SylowC11 ⋊ D5×C17×D9
SylowC9 ⋊ C2×C17×D55
SylowC5 ⋊ C17×D9×D11

Subgroups

subgroupG/H
center, hypercenterC17D9×D55
commutator, cosocle, hypocenterC5×C9×C11C22×C17
FrattiniC3D3×C17×D55
FittingC5×C9×C11×C17C22
socleC3×C5×C11×C17C2×D3
LCSG ▷ C5×C9×C11
UCSC1 ◁ C17

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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

2958 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 97);