Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2601 |
| unambiguous semidirect product | C9⋊(C5×D289) |
| unambiguous semidirect product | C289⋊(C5×D9) |
| Fitting, Hall | C5×C9×C289 ⋊ C2 |
| derived, Hall | C9×C289 ⋊ C2×C5 |
| Hall | C5×C289 ⋊ D9 |
| Sylow | C289 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ D289 |
| Sylow | C9 ⋊ C5×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2601 |
| commutator, cosocle, hypocenter | C9×C289 | C2×C5 |
| Frattini | C3×C17 | C5×D51 |
| Fitting | C5×C9×C289 | C2 |
| socle | C3×C5×C17 | D51 |
| LCS | G ▷ C9×C289 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13005 |
6510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 6);