Finite Group DatabasebetaFinite Group Databasebeta| order | 26505 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19127102⋊C5 |
| derived, Hall | C19×C31 ⋊ C5×C9 |
| Hall | #19127102 ⋊ C5 |
| Hall | C19×ΓL(1,𝔽32) ⋊ C9 |
| Hall | ΓL(1,𝔽32) ⋊ #4294 |
| Sylow | C31 ⋊ C5×#4294 |
| Sylow | C19 ⋊ ΓL(1,𝔽32)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #13183715⋊C5 |
| commutator, hypocenter | C19×C31 | C5×C9 |
| Fitting, socle, cosocle | C3×C19×C31 | C3×C5 |
| prime radical | C3×C19×ΓL(1,𝔽32) | C3 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5301 |
Polycyclic presentation:
3,5,19,31,3|a^3=e,c^a=c^7,d^a=d^25,d^b=d^16249 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26505, 9);