Finite Group Databasebeta

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C29×D585 #46800230

order33930
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D585
unambiguous semidirect productC5⋊(C29×D117)
unambiguous semidirect productC9⋊(C29×D65)
unambiguous semidirect productC13⋊(C29×D45)

Splittings

Fitting, HallC5×C9×C13×C29 ⋊ C2
derived, HallC5×C9×C13 ⋊ C2×C29
HallC9×C13×C29 ⋊ D5
HallC5×C13×C29 ⋊ D9
HallC5×C9×C29 ⋊ D13
HallC13×C29 ⋊ D45
HallC9×C29 ⋊ D65
HallC5×C29 ⋊ D117
HallC9×C13 ⋊ D5×C29
HallC5×C13 ⋊ D9×C29
HallC5×C9 ⋊ D13×C29
SylowC13 ⋊ C29×D45
SylowC9 ⋊ C29×D65
SylowC5 ⋊ C29×D117

Subgroups

subgroupG/H
center, hypercenterC29D585
commutator, cosocle, hypocenterC5×C9×C13C2×C29
FrattiniC3C29×D195
FittingC5×C9×C13×C29C2
socleC3×C5×C13×C29D3
LCSG ▷ C5×C9×C13
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16965

Conjugacy classes & character table

8526 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 16);