Finite Group Databasebeta

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C9×D1105 #34091024

order19890
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D1105
unambiguous semidirect productC5⋊(C9×D221)
unambiguous semidirect productC17⋊(C9×D65)

Splittings

Fitting, HallC5×C9×C13×C17 ⋊ C2
derived, HallC5×C13×C17 ⋊ C2×C9
HallC9×C13×C17 ⋊ D5
HallC5×C9×C17 ⋊ D13
HallC5×C9×C13 ⋊ D17
HallC13×C17 ⋊ C9×D5
HallC9×C17 ⋊ D65
HallC9×C13 ⋊ D85
HallC5×C17 ⋊ C9×D13
HallC5×C13 ⋊ C9×D17
HallC5×C9 ⋊ D221
SylowC17 ⋊ C9×D65
SylowC13 ⋊ C9×D85
SylowC5 ⋊ C9×D221

Subgroups

subgroupG/H
center, hypercenterC9D1105
commutator, hypocenterC5×C13×C17C2×C9
FrattiniC3C3×D1105
FittingC5×C9×C13×C17C2
socle, cosocleC3×C5×C13×C17C2×C3
prime radicalC3×D1105C3
LCSG ▷ C5×C13×C17
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

4986 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 9);