Finite Group DatabasebetaFinite Group Databasebeta| order | 31545 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C701⋊C5 |
| unambiguous semidirect product | C701⋊(C32×C5) |
| unambiguous semidirect product | (C3×C701)⋊(C3×C5) |
| unambiguous semidirect product | (C32×C701)⋊C5 |
| Fitting, socle, Hall | C32×C701 ⋊ C5 |
| derived, Sylow | C701 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C701⋊C5 |
| commutator, cosocle, hypocenter | C701 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C701 | C5 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C32 | |
24 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, 4);