Finite Group Databasebeta

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C2×C5×C7×D9×C29 #49141315

order36540
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D9×C29
unambiguous semidirect productC9⋊(C22×C5×C7×C29)
unambiguous semidirect product(C2×C9)⋊(C2×C5×C7×C29)

Splittings

FittingC2×C5×C7×C9×C29 ⋊ C2
derived, SylowC9 ⋊ C22×C5×C7×C29
HallC5×C7×C9×C29 ⋊ C22
HallC7×C9×C29 ⋊ C22×C5
HallC5×C9×C29 ⋊ C22×C7
HallC5×C7×C9 ⋊ C22×C29
HallC9×C29 ⋊ C22×C5×C7
HallC7×C9 ⋊ C22×C5×C29
HallC5×C9 ⋊ C22×C7×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C29D9
commutator, cosocle, hypocenterC9C22×C5×C7×C29
FrattiniC3C2×C5×D3×C7×C29
FittingC2×C5×C7×C9×C29C2
socleC2×C3×C5×C7×C29D3
LCSG ▷ C9
UCSC1 ◁ C2×C5×C7×C29

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18270

Conjugacy classes & character table

12180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 157);