Finite Group Databasebeta

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D9×D1001 #49114491

order36036
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD9×D1001
unambiguous semidirect product(C7×D9)⋊D143
unambiguous semidirect product(C11×D9)⋊D91
unambiguous semidirect product(C13×D9)⋊D77

Splittings

Fitting, derived, HallC7×C9×C11×C13 ⋊ C22
HallC9×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×D9
HallC7×C9×C13 ⋊ C2×D11
HallC7×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ D7×D9
HallC9×C13 ⋊ C2×D77
HallC9×C11 ⋊ C2×D91
HallC7×C13 ⋊ D9×D11
HallC7×C11 ⋊ D9×D13
HallC7×C9 ⋊ C2×D143
SylowC13 ⋊ D9×D77
SylowC11 ⋊ D9×D91
SylowC9 ⋊ C2×D1001
SylowC7 ⋊ D9×D143

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C9×C11×C13C22
FrattiniC3D3×D1001
socleC3×C7×C11×C13C2×D3
LCSG ▷ C7×C9×C11×C13
UCSC1

120 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 37 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) = 9009

Conjugacy classes & character table

3012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 159);