Finite Group Databasebeta

C5×C23×D13⋊C9 #41002092

order26910
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×D13⋊C9
unambiguous semidirect productD13⋊(C5×C9×C23)
unambiguous semidirect product(C13⋊C9)⋊(C2×C5×C23)
unambiguous semidirect product(C5×D13)⋊(C9×C23)
unambiguous semidirect product(C23×D13)⋊(C5×C9)
unambiguous semidirect product(C5×C23×D13)⋊C9

Splittings

derived, SylowC13 ⋊ C2×C5×C9×C23
HallC5×C23×C13⋊C9 ⋊ C2
HallC5×C23×D13 ⋊ C9
HallC23×C13⋊C9 ⋊ C2×C5
HallC5×C13×C23 ⋊ C2×C9
HallC23×D13 ⋊ C5×C9
HallC5×C13⋊C9 ⋊ C2×C23
HallC13×C23 ⋊ C2×C5×C9
HallC5×D13 ⋊ C9×C23
HallC13⋊C9 ⋊ C2×C5×C23
HallC5×C13 ⋊ C2×C9×C23
HallD13 ⋊ C5×C9×C23

Subgroups

subgroupG/H
center, hypercenterC3×C5×C23D13⋊C3
commutator, hypocenterC13C2×C5×C9×C23
FrattiniC3C5×C23×D13⋊C3
Fitting, socleC3×C5×C13×C23C2×C3
prime radicalC3×C5×C23×D13C3
cosocleC3×C13C2×C3×C5×C23
LCSG ▷ C13
UCSC1 ◁ C3×C5×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

2760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 19);