Finite Group Databasebeta

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C5×C9×D71⋊C5 #44544029

order31950
automorphism?
homologyAbelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×C9×D71⋊C5
unambiguous semidirect productD71⋊(C52×C9)
unambiguous semidirect product(C71⋊C5)⋊(C2×C5×C9)
unambiguous semidirect product(C5×D71)⋊(C5×C9)
unambiguous semidirect product(C9×D71)⋊C52
unambiguous semidirect product(C5×C9×D71)⋊C5

Splittings

FittingC5×C9×C71 ⋊ C2×C5
derived, SylowC71 ⋊ C2×C52×C9
HallC5×C9×C71⋊C5 ⋊ C2
HallC5×C71⋊C5 ⋊ C2×C9
HallC9×D71 ⋊ C52
HallC9×C71 ⋊ C2×C52
HallD71 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9D71⋊C5
commutator, hypocenterC71C2×C52×C9
FrattiniC3C3×C5×D71⋊C5
FittingC5×C9×C71C2×C5
socleC3×C5×C71C2×C3×C5
prime radicalC3×C5×D71⋊C5C3
cosocleC3×C71C2×C3×C52
LCSG ▷ C71
UCSC1 ◁ C5×C9

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 32);