Finite Group Databasebeta

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C9×D1495 #41002082

order26910
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D1495
unambiguous semidirect productC5⋊(C9×D299)
unambiguous semidirect productC23⋊(C9×D65)

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, HallC5×C13×C23 ⋊ C2×C9
HallC9×C13×C23 ⋊ D5
HallC5×C9×C23 ⋊ D13
HallC5×C9×C13 ⋊ D23
HallC13×C23 ⋊ C9×D5
HallC9×C23 ⋊ D65
HallC9×C13 ⋊ D115
HallC5×C23 ⋊ C9×D13
HallC5×C13 ⋊ C9×D23
HallC5×C9 ⋊ D299
SylowC23 ⋊ C9×D65
SylowC13 ⋊ C9×D115
SylowC5 ⋊ C9×D299

Subgroups

subgroupG/H
center, hypercenterC9D1495
commutator, hypocenterC5×C13×C23C2×C9
FrattiniC3C3×D1495
FittingC5×C9×C13×C23C2
socle, cosocleC3×C5×C13×C23C2×C3
prime radicalC3×D1495C3
LCSG ▷ C5×C13×C23
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6741 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 9);