Finite Group Databasebeta

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C5×C9×D299 #41002078

order26910
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D299
unambiguous semidirect productC23⋊(C5×C9×D13)

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, HallC13×C23 ⋊ C2×C5×C9
HallC9×C13×C23 ⋊ C2×C5
HallC5×C13×C23 ⋊ C2×C9
HallC5×C9×C23 ⋊ D13
HallC5×C9×C13 ⋊ D23
HallC9×C23 ⋊ C5×D13
HallC9×C13 ⋊ C5×D23
HallC5×C23 ⋊ C9×D13
HallC5×C13 ⋊ C9×D23
SylowC23 ⋊ C5×C9×D13
SylowC13 ⋊ C5×C9×D23

Subgroups

subgroupG/H
center, hypercenterC5×C9D299
commutator, hypocenterC13×C23C2×C5×C9
FrattiniC3C3×C5×D299
FittingC5×C9×C13×C23C2
socleC3×C5×C13×C23C2×C3
prime radicalC3×C5×D299C3
cosocleC3×C13×C23C2×C3×C5
LCSG ▷ C13×C23
UCSC1 ◁ C5×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6795 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 5);