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C3⋊(C5⋊(C17⋊(D13⋊C3))) #34091053

order19890
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C5⋊(C17⋊(D13⋊C3)))
unambiguous semidirect productC5⋊(C3⋊(C17⋊(D13⋊C3)))
unambiguous semidirect productC17⋊(C3⋊(C5⋊(D13⋊C3)))
unambiguous semidirect product(C13⋊C3)⋊D255
unambiguous semidirect productD3315⋊C3

Splittings

Fitting, socle, derivedC3×C5×C13×C17 ⋊ C2×C3
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC3×C17×C13⋊C3 ⋊ D5
HallC5×C13×C17 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ D17
HallC13×C17 ⋊ C3×D15
HallC3×C13⋊C3 ⋊ D85
HallC5×C17 ⋊ C3⋊(D13⋊C3)
HallC5×C13 ⋊ C3×D51
SylowC17 ⋊ C3⋊(C5⋊(D13⋊C3))
SylowC13 ⋊ C3×D255
SylowC5 ⋊ C3⋊(C17⋊(D13⋊C3))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C17C2×C3
LCSG ▷ C3×C5×C13×C17
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Polycyclic presentation:

2,3^2,5,13,17|c^a=c^2,d^a=d^4,e^a=e^12,f^a=f^16,e^b=e^3

Conjugacy classes & character table

897 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 38);