Finite Group Databasebeta

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C9×C17×C41⋊C5 #44535851

order31365
automorphism?
homologyAbelianization (H1) = C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC9×C17×C41⋊C5
unambiguous semidirect productC41⋊(C5×C9×C17)
unambiguous semidirect product(C9×C41)⋊(C5×C17)
unambiguous semidirect product(C17×C41)⋊(C5×C9)
unambiguous semidirect product(C9×C17×C41)⋊C5

Splittings

Fitting, HallC9×C17×C41 ⋊ C5
derived, SylowC41 ⋊ C5×C9×C17
HallC17×C41 ⋊ C5×C9
HallC9×C41 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC9×C17C41⋊C5
commutator, hypocenterC41C5×C9×C17
FrattiniC3C3×C17×C41⋊C5
FittingC9×C17×C41C5
socleC3×C17×C41C3×C5
prime radicalC3×C17×C41⋊C5C3
cosocleC3×C41C3×C5×C17
LCSG ▷ C41
UCSC1 ◁ C9×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6273

Conjugacy classes & character table

1989 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31365, 2);