Finite Group DatabasebetaFinite Group Databasebeta| order | 35715 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C2381⋊C5 |
| unambiguous semidirect product | C2381⋊(C3×C5) |
| unambiguous semidirect product | (C3×C2381)⋊C5 |
| Fitting, socle, Hall | C3×C2381 ⋊ C5 |
| derived, Sylow | C2381 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C2381⋊C5 |
| commutator, cosocle, hypocenter | C2381 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C2381 | C5 |
| LCS | G ▷ C2381 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7143 |
1443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35715, 1);