Finite Group Databasebeta

← Prev (#46777900) Next (#46777902) →

C5×C17×D9×D11 #46777901

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

Aliases

direct productC5×C17×D9×D11

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C22
derived, HallC9×C11 ⋊ C22×C5×C17
HallC9×C11×C17 ⋊ C22×C5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C17 ⋊ C2×D11
HallC5×C9×C11 ⋊ C22×C17
HallC11×C17 ⋊ C2×C5×D9
HallC9×C17 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×C17×D9
HallC5×C9 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C5×C17×D9
SylowC9 ⋊ C2×C5×C17×D11

Subgroups

subgroupG/H
center, hypercenterC5×C17D9×D11
commutator, cosocle, hypocenterC9×C11C22×C5×C17
FrattiniC3C5×D3×C17×D11
FittingC5×C9×C11×C17C22
socleC3×C5×C11×C17C2×D3
LCSG ▷ C9×C11
UCSC1 ◁ C5×C17

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 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

3570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 69);