Finite Group Databasebeta

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C9×C5⋊(D71⋊C5) #44544030

order31950
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C5⋊(D71⋊C5)
unambiguous semidirect productC5⋊(C9×D71⋊C5)
unambiguous semidirect product(C71⋊C5)⋊(C9×D5)
unambiguous semidirect productD355⋊(C5×C9)
unambiguous semidirect product(C9×D355)⋊C5

Splittings

FittingC5×C9×C71 ⋊ C2×C5
derivedC5×C71 ⋊ C2×C5×C9
HallC5×C9×C71⋊C5 ⋊ C2
HallC5×C71⋊C5 ⋊ C2×C9
HallC9×C71 ⋊ C5×D5
SylowC71 ⋊ C5×C9×D5

Subgroups

subgroupG/H
center, hypercenterC9C5⋊(D71⋊C5)
commutator, hypocenterC5×C71C2×C5×C9
FrattiniC3C3×C5⋊(D71⋊C5)
FittingC5×C9×C71C2×C5
socle, cosocleC3×C5×C71C2×C3×C5
prime radicalC3×C5⋊(D71⋊C5)C3
LCSG ▷ C5×C71
UCSC1 ◁ C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 33);