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D39⋊(D41⋊C5) #44544337

order31980
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD39⋊(D41⋊C5)
unambiguous semidirect product(C3⋊(D41⋊C5))⋊D13
unambiguous semidirect product(C13⋊(D41⋊C5))⋊D3
unambiguous semidirect product(D39⋊D41)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C41 ⋊ C22×C5
HallC3×C13×C41⋊C5 ⋊ C22
HallD39⋊D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×D3
HallC3×C41⋊C5 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC41⋊C5 ⋊ D3×D13
HallC3×C41 ⋊ C2×C5×D13
SylowC41 ⋊ C5×D3×D13
HallC3×C13 ⋊ C2×D41⋊C5
SylowC13 ⋊ D3×D41⋊C5
SylowC3 ⋊ D13×D41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C41C22×C5
LCSG ▷ C3×C13×C41
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Polycyclic presentation:

2^2,5,3,13,41|e^a=e^12,f^a=f^40,d^b=d^2,e^b=e^12,f^c=f^10

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 65);