Finite Group Databasebeta

← Prev (#46800243) Next (#46800245) →

C3×C5⋊(C29⋊(D13⋊C3)) #46800244

order33930
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊(C29⋊(D13⋊C3))
unambiguous semidirect productC5⋊(C3×C29⋊(D13⋊C3))
unambiguous semidirect productC29⋊(C3×C5⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊(C3×D145)
unambiguous semidirect productD1885⋊C32
unambiguous semidirect product(C3×D1885)⋊C3

Splittings

Fitting, socleC3×C5×C13×C29 ⋊ C2×C3
derived, HallC5×C13×C29 ⋊ C2×C32
HallC3×C5×C29×C13⋊C3 ⋊ C2
HallD1885 ⋊ C32
HallC3×C29×C13⋊C3 ⋊ D5
HallC3×C5×C13⋊C3 ⋊ D29
HallC13×C29 ⋊ C32×D5
HallC5×C29 ⋊ C3×D13⋊C3
HallC3×C13⋊C3 ⋊ D145
HallC5×C13 ⋊ C32×D29
SylowC29 ⋊ C3×C5⋊(D13⋊C3)
SylowC13 ⋊ C32×D145
SylowC5 ⋊ C3×C29⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C29⋊(D13⋊C3))
commutator, cosocle, hypocenterC5×C13×C29C2×C32
FrattiniC1G
Fitting, socleC3×C5×C13×C29C2×C3
LCSG ▷ C5×C13×C29
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5655

Conjugacy classes & character table

1536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 30);