Finite Group DatabasebetaFinite Group Databasebeta| order | 31545 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C701⋊C5 |
| unambiguous semidirect product | C701⋊(C5×C9) |
| unambiguous semidirect product | (C9×C701)⋊C5 |
| Fitting, Hall | C9×C701 ⋊ C5 |
| derived, Sylow | C701 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C701⋊C5 |
| commutator, hypocenter | C701 | C5×C9 |
| Frattini | C3 | C3×C701⋊C5 |
| Fitting | C9×C701 | C5 |
| socle, cosocle | C3×C701 | C3×C5 |
| prime radical | C3×C701⋊C5 | C3 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6309 |
1305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31545, 2);