Finite Group DatabasebetaFinite Group Databasebeta| order | 26820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D5×D149 |
| unambiguous semidirect product | (D5×C149)⋊(C2×C9) |
| unambiguous semidirect product | (C5×D149)⋊(C2×C9) |
| unambiguous semidirect product | D745⋊(C2×C9) |
| Fitting, Hall | C5×C9×C149 ⋊ C22 |
| derived, Hall | C5×C149 ⋊ C22×C9 |
| Hall | C9×C149 ⋊ C2×D5 |
| Sylow | C149 ⋊ C2×C9×D5 |
| Hall | C5×C9 ⋊ C2×D149 |
| Sylow | C5 ⋊ C2×C9×D149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D5×D149 |
| commutator, hypocenter | C5×C149 | C22×C9 |
| Frattini | C3 | C3×D5×D149 |
| Fitting | C5×C9×C149 | C22 |
| socle, cosocle | C3×C5×C149 | C22×C3 |
| prime radical | C3×D5×D149 | C3 |
| LCS | G ▷ C5×C149 | |
| UCS | C1 ◁ C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6705 |
2736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 16);