Finite Group Databasebeta

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C3⋊(C5⋊(C29⋊(D13⋊C3))) #46800252

order33930
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C5⋊(C29⋊(D13⋊C3)))
unambiguous semidirect productC5⋊(C3⋊(C29⋊(D13⋊C3)))
unambiguous semidirect productC29⋊(C3⋊(C5⋊(D13⋊C3)))
unambiguous semidirect product(C13⋊C3)⋊D435
unambiguous semidirect productD5655⋊C3

Splittings

Fitting, socle, derivedC3×C5×C13×C29 ⋊ C2×C3
HallC3×C5×C29×C13⋊C3 ⋊ C2
HallC3×C29×C13⋊C3 ⋊ D5
HallC5×C13×C29 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ D29
HallC13×C29 ⋊ C3×D15
HallC5×C29 ⋊ C3⋊(D13⋊C3)
HallC3×C13⋊C3 ⋊ D145
HallC5×C13 ⋊ C3×D87
SylowC29 ⋊ C3⋊(C5⋊(D13⋊C3))
SylowC13 ⋊ C3×D435
SylowC5 ⋊ C3⋊(C29⋊(D13⋊C3))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C29C2×C3
LCSG ▷ C3×C5×C13×C29
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5655

Polycyclic presentation:

2,3^2,5,13,29|c^a=c^2,d^a=d^4,e^a=e^12,f^a=f^28,e^b=e^3

Conjugacy classes & character table

1527 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 38);