Finite Group Databasebeta

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C5×C23⋊(D13⋊C9) #41002093

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

Aliases

direct productC5×C23⋊(D13⋊C9)
unambiguous semidirect productC23⋊(C5×D13⋊C9)
unambiguous semidirect product(C13⋊C9)⋊(C5×D23)
unambiguous semidirect productD299⋊(C5×C9)
unambiguous semidirect product(C5×D299)⋊C9

Splittings

derived, HallC13×C23 ⋊ C2×C5×C9
HallC5×C23×C13⋊C9 ⋊ C2
HallC5×D299 ⋊ C9
HallC23×C13⋊C9 ⋊ C2×C5
HallC5×C13×C23 ⋊ C2×C9
HallD299 ⋊ C5×C9
HallC5×C13⋊C9 ⋊ D23
HallC13⋊C9 ⋊ C5×D23
HallC5×C23 ⋊ D13⋊C9
HallC5×C13 ⋊ C9×D23
SylowC23 ⋊ C5×D13⋊C9
SylowC13 ⋊ C5×C9×D23

Subgroups

subgroupG/H
center, hypercenterC3×C5C23⋊(D13⋊C3)
commutator, hypocenterC13×C23C2×C5×C9
FrattiniC3C5×C23⋊(D13⋊C3)
Fitting, socleC3×C5×C13×C23C2×C3
prime radicalC3×C5×D299C3
cosocleC3×C13×C23C2×C3×C5
LCSG ▷ C13×C23
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 20);