Finite Group DatabasebetaFinite Group Databasebeta| order | 26505 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19127106⋊C5 |
| Fitting, socle, derived, Hall | C19×C31 ⋊ C5×C9 |
| Hall | #19127106 ⋊ C5 |
| Hall | C19×ΓL(1,𝔽32) ⋊ C9 |
| Hall | ΓL(1,𝔽32) ⋊ #4296 |
| Sylow | C31 ⋊ C5×#4296 |
| Sylow | C19 ⋊ ΓL(1,𝔽32)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C31 | C5×C9 |
| prime radical | C19⋊C3×ΓL(1,𝔽32) | C3 |
| cosocle | C31×C19⋊C3 | C3×C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 589 |
Polycyclic presentation:
3,5,3,19,31|a^3=c,d^a=d^4,e^a=e^25,e^b=e^16,d^c=d^773 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26505, 13);