Finite Group DatabasebetaFinite Group Databasebeta| order | 26505 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#19127106 |
| Fitting, socle, Hall | C5×C19×C31 ⋊ C9 |
| derived, Hall | C19×C31 ⋊ C5×C9 |
| Hall | C5×C31 ⋊ #4296 |
| Hall | C5×C19 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ C5×#4296 |
| Sylow | C19 ⋊ C5×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #19127106 |
| commutator, hypocenter | C19×C31 | C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C31 | C9 |
| prime radical | C5×C31×C19⋊C3 | C3 |
| cosocle | C31×C19⋊C3 | C3×C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2945 |
505 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26505, 22);