Finite Group Databasebeta

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C9×C23×D65 #41002081

order26910
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC9×C23×D65
unambiguous semidirect productC5⋊(C9×C23×D13)

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, HallC5×C13 ⋊ C2×C9×C23
HallC9×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ C2×C9
HallC5×C9×C23 ⋊ D13
HallC5×C9×C13 ⋊ C2×C23
HallC13×C23 ⋊ C9×D5
HallC9×C13 ⋊ D5×C23
HallC5×C23 ⋊ C9×D13
HallC5×C9 ⋊ C23×D13
SylowC13 ⋊ C9×D5×C23
SylowC5 ⋊ C9×C23×D13

Subgroups

subgroupG/H
center, hypercenterC9×C23D65
commutator, hypocenterC5×C13C2×C9×C23
FrattiniC3C3×C23×D65
FittingC5×C9×C13×C23C2
socleC3×C5×C13×C23C2×C3
prime radicalC3×C23×D65C3
cosocleC3×C5×C13C2×C3×C23
LCSG ▷ C5×C13
UCSC1 ◁ C9×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

7038 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 8);