Finite Group Databasebeta

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C5×C7×C29×C22⋊C9 #49141306

order36540
automorphism?
homologyAbelianization (H1) = C5×C7×C9×C29 · Schur multiplier (H2) = C2

Aliases

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

Splittings

derived, SylowC22 ⋊ C5×C7×C9×C29
HallC22×C5×C7×C29 ⋊ C9
HallC22×C7×C29 ⋊ C5×C9
HallC22×C5×C29 ⋊ C7×C9
HallC22×C5×C7 ⋊ C9×C29
HallC22×C29 ⋊ C5×C7×C9
HallC22×C7 ⋊ C5×C9×C29
HallC22×C5 ⋊ C7×C9×C29

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7×C29A4
commutator, hypocenterC22C5×C7×C9×C29
FrattiniC3C5×C7×A4×C29
Fitting, socle, prime radicalC22×C3×C5×C7×C29C3
cosocleC22×C3C3×C5×C7×C29
LCSG ▷ C22
UCSC1 ◁ C3×C5×C7×C29

64 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, 148);