Finite Group Databasebeta

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C9×C13×D115 #41002080

order26910
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×C13×D115
unambiguous semidirect productC5⋊(C9×C13×D23)
unambiguous semidirect productC23⋊(C9×D5×C13)

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, HallC5×C23 ⋊ C2×C9×C13
HallC9×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ C2×C9
HallC5×C9×C23 ⋊ C2×C13
HallC5×C9×C13 ⋊ D23
HallC13×C23 ⋊ C9×D5
HallC9×C23 ⋊ D5×C13
HallC5×C13 ⋊ C9×D23
HallC5×C9 ⋊ C13×D23
SylowC23 ⋊ C9×D5×C13
SylowC5 ⋊ C9×C13×D23

Subgroups

subgroupG/H
center, hypercenterC9×C13D115
commutator, hypocenterC5×C23C2×C9×C13
FrattiniC3C3×C13×D115
FittingC5×C9×C13×C23C2
socleC3×C5×C13×C23C2×C3
prime radicalC3×C13×D115C3
cosocleC3×C5×C23C2×C3×C13
LCSG ▷ C5×C23
UCSC1 ◁ C9×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6903 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 7);