Finite Group Databasebeta

C23×C5⋊(D13⋊C9) #41002096

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

Aliases

direct productC23×C5⋊(D13⋊C9)
unambiguous semidirect productC5⋊(C23×D13⋊C9)
unambiguous semidirect product(C13⋊C9)⋊(D5×C23)
unambiguous semidirect productD65⋊(C9×C23)
unambiguous semidirect product(C23×D65)⋊C9

Splittings

derived, HallC5×C13 ⋊ C2×C9×C23
HallC5×C23×C13⋊C9 ⋊ C2
HallC23×D65 ⋊ C9
HallC23×C13⋊C9 ⋊ D5
HallC5×C13×C23 ⋊ C2×C9
HallC5×C13⋊C9 ⋊ C2×C23
HallC13×C23 ⋊ C9×D5
HallD65 ⋊ C9×C23
HallC13⋊C9 ⋊ D5×C23
HallC5×C23 ⋊ D13⋊C9
SylowC13 ⋊ C9×D5×C23
SylowC5 ⋊ C23×D13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C23C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C2×C9×C23
FrattiniC3C23×C5⋊(D13⋊C3)
Fitting, socleC3×C5×C13×C23C2×C3
prime radicalC3×C23×D65C3
cosocleC3×C5×C13C2×C3×C23
LCSG ▷ C5×C13
UCSC1 ◁ C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 23);