Finite Group DatabasebetaFinite Group Databasebeta| order | 26586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(D211⋊C7) |
| unambiguous semidirect product | (C211⋊C7)⋊D9 |
| unambiguous semidirect product | D1899⋊C7 |
| Fitting, derived, Hall | C9×C211 ⋊ C2×C7 |
| Hall | C9×C211⋊C7 ⋊ C2 |
| Hall | D1899 ⋊ C7 |
| Hall | C211⋊C7 ⋊ D9 |
| Sylow | C211 ⋊ C7×D9 |
| Sylow | C9 ⋊ D211⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C211 | C2×C7 |
| Frattini | C3 | C3⋊(D211⋊C7) |
| socle | C3×C211 | D3×C7 |
| LCS | G ▷ C9×C211 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1899 |
Polycyclic presentation:
2,3,7,211,3|b^3=e^2,b^a=b^2e,d^a=d^210,e^a=e^2,d^c=d^171177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26586, 17);