Finite Group DatabasebetaFinite Group Databasebeta| order | 26049 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C457⋊C19 |
| unambiguous semidirect product | (C3×C457)⋊C19 |
| Fitting, socle, Hall | C3×C457 ⋊ C19 |
| derived, Sylow | C457 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C457⋊C19 |
| commutator, cosocle, hypocenter | C457 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C457 | C19 |
| LCS | G ▷ C457 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1371 |
129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26049, 2);