Finite Group DatabasebetaFinite Group Databasebeta| order | 26049 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C457⋊C3)⋊C19 |
| unambiguous semidirect product | (C457⋊C19)⋊C3 |
| Fitting, socle, derived, Sylow | C457 ⋊ C3×C19 |
| Hall | C457⋊C19 ⋊ C3 |
| Hall | C457⋊C3 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C457 | C3×C19 |
| LCS | G ▷ C457 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 457 |
Polycyclic presentation:
3,19,457|c^a=c^323,c^b=c^34765 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26049, 1);