Finite Group Databasebeta

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C5×C9⋊(D71⋊C5) #44544032

order31950
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C9⋊(D71⋊C5)
unambiguous semidirect productC9⋊(C5×D71⋊C5)
unambiguous semidirect product(C71⋊C5)⋊(C5×D9)
unambiguous semidirect productD639⋊C52
unambiguous semidirect product(C5×D639)⋊C5

Splittings

FittingC5×C9×C71 ⋊ C2×C5
derived, HallC9×C71 ⋊ C2×C52
HallC5×C9×C71⋊C5 ⋊ C2
HallC5×C71⋊C5 ⋊ D9
HallD639 ⋊ C52
SylowC71 ⋊ C52×D9
SylowC9 ⋊ C5×D71⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C9⋊(D71⋊C5)
commutator, cosocle, hypocenterC9×C71C2×C52
FrattiniC3C5×C3⋊(D71⋊C5)
FittingC5×C9×C71C2×C5
socleC3×C5×C71C5×D3
LCSG ▷ C9×C71
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 35);