Finite Group Databasebeta

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C7×D5×D9×C29 #49141289

order36540
automorphism?
homologyAbelianization (H1) = C22×C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×D9×C29
unambiguous semidirect product(C5×D9)⋊(C2×C7×C29)
unambiguous semidirect product(C9×D5)⋊(C2×C7×C29)
unambiguous semidirect productD45⋊(C2×C7×C29)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C22
derived, HallC5×C9 ⋊ C22×C7×C29
HallC7×C9×C29 ⋊ C2×D5
HallC5×C9×C29 ⋊ C22×C7
HallC5×C7×C29 ⋊ C2×D9
HallC5×C7×C9 ⋊ C22×C29
HallC9×C29 ⋊ C2×C7×D5
HallC5×C29 ⋊ C2×C7×D9
HallC7×C9 ⋊ C2×D5×C29
HallC5×C7 ⋊ C2×D9×C29
SylowC9 ⋊ C2×C7×D5×C29
SylowC5 ⋊ C2×C7×D9×C29

Subgroups

subgroupG/H
center, hypercenterC7×C29D5×D9
commutator, cosocle, hypocenterC5×C9C22×C7×C29
FrattiniC3D3×C7×D5×C29
FittingC5×C7×C9×C29C22
socleC3×C5×C7×C29C2×D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C29

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) = 9135

Conjugacy classes & character table

4872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 131);