Finite Group Databasebeta

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C5×C29×C22⋊(C7⋊C9) #49141305

order36540
automorphism?
homologyAbelianization (H1) = C5×C9×C29 · Schur multiplier (H2) = C2

Aliases

direct productC5×C29×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C5×C29×C7⋊C9)
unambiguous semidirect productC7⋊(C5×C29×C22⋊C9)
unambiguous semidirect product(C22×C5)⋊(C29×C7⋊C9)
unambiguous semidirect product(C5×C7)⋊(C29×C22⋊C9)
unambiguous semidirect product(C22×C29)⋊(C5×C7⋊C9)
unambiguous semidirect product(C7×C29)⋊(C5×C22⋊C9)
unambiguous semidirect product(C22×C5×C29)⋊(C7⋊C9)
unambiguous semidirect product(C5×C7×C29)⋊(C22⋊C9)

Splittings

derived, HallC22×C7 ⋊ C5×C9×C29
HallC22×C5×C7×C29 ⋊ C9
HallC5×C7×C29 ⋊ C22⋊C9
HallC22×C7×C29 ⋊ C5×C9
HallC22×C5×C29 ⋊ C7⋊C9
HallC7×C29 ⋊ C5×C22⋊C9
HallC22×C5×C7 ⋊ C9×C29
HallC22×C29 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C29×C22⋊C9
HallC22×C5 ⋊ C29×C7⋊C9
SylowC7 ⋊ C5×C29×C22⋊C9
SylowC22 ⋊ C5×C29×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5×C29C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C5×C9×C29
FrattiniC3C5×C29×C22⋊ΓL(1,𝔽8)
Fitting, socle, prime radicalC22×C3×C5×C7×C29C3
cosocleC22×C3×C7C3×C5×C29
LCSG ▷ C22×C7
UCSC1 ◁ C3×C5×C29

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18270

Conjugacy classes & character table

5220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 147);