Finite Group DatabasebetaFinite Group Databasebeta| order | 32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D865 |
| unambiguous semidirect product | C5⋊(C19×D173) |
| unambiguous semidirect product | C173⋊(D5×C19) |
| Fitting, socle, Hall | C5×C19×C173 ⋊ C2 |
| derived, Hall | C5×C173 ⋊ C2×C19 |
| Hall | C19×C173 ⋊ D5 |
| Sylow | C173 ⋊ D5×C19 |
| Hall | C5×C19 ⋊ D173 |
| Sylow | C5 ⋊ C19×D173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D865 |
| commutator, cosocle, hypocenter | C5×C173 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C173 | C2 |
| LCS | G ▷ C5×C173 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16435 |
8246 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32870, 6);