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C3⋊(C17⋊(D41⋊C5)) #35229986

order20910
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C17⋊(D41⋊C5))
unambiguous semidirect productC17⋊(C3⋊(D41⋊C5))
unambiguous semidirect product(C41⋊C5)⋊D51
unambiguous semidirect productD2091⋊C5

Splittings

Fitting, socle, derived, HallC3×C17×C41 ⋊ C2×C5
HallC3×C17×C41⋊C5 ⋊ C2
HallD2091 ⋊ C5
HallC17×C41⋊C5 ⋊ D3
HallC17×C41 ⋊ C5×D3
HallC3×C41⋊C5 ⋊ D17
HallC41⋊C5 ⋊ D51
HallC3×C41 ⋊ C5×D17
HallC3×C17 ⋊ D41⋊C5
SylowC41 ⋊ C5×D51
SylowC17 ⋊ C3⋊(D41⋊C5)
SylowC3 ⋊ C17⋊(D41⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C17×C41C2×C5
LCSG ▷ C3×C17×C41
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2091

Polycyclic presentation:

2,3,5,17,41|b^a=b^2,d^a=d^16,e^a=e^40,e^c=e^10

Conjugacy classes & character table

339 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20910, 24);