Finite Group Databasebeta

← Prev (#44544063) Next (#44544065) →

C3⋊(C3⋊(C5⋊(D71⋊C5))) #44544064

order31950
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(C5⋊(D71⋊C5)))
unambiguous semidirect productC5⋊(C3⋊(C3⋊(D71⋊C5)))
unambiguous semidirect product(C71⋊C5)⋊(C3⋊D15)
unambiguous semidirect product(C3⋊D1065)⋊C5

Splittings

Fitting, socle, derivedC32×C5×C71 ⋊ C2×C5
HallC32×C5×C71⋊C5 ⋊ C2
HallC5×C71⋊C5 ⋊ C3⋊D3
HallC32×C71 ⋊ C5×D5
SylowC71 ⋊ C5×C3⋊D15
SylowC32 ⋊ C5⋊(D71⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C71C2×C5
LCSG ▷ C32×C5×C71
UCSC1

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Polycyclic presentation:

2,5,3^2,5,71|c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^70,f^b=f^57

Conjugacy classes & character table

435 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 67);