Finite Group DatabasebetaFinite Group Databasebeta| order | 32470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D191⋊C5) |
| unambiguous semidirect product | (C191⋊C5)⋊D17 |
| unambiguous semidirect product | D3247⋊C5 |
| Fitting, socle, derived, Hall | C17×C191 ⋊ C2×C5 |
| Hall | C17×C191⋊C5 ⋊ C2 |
| Hall | D3247 ⋊ C5 |
| Hall | C191⋊C5 ⋊ D17 |
| Sylow | C191 ⋊ C5×D17 |
| Sylow | C17 ⋊ D191⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C191 | C2×C5 |
| LCS | G ▷ C17×C191 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3247 |
Polycyclic presentation:
2,5,17,191|c^a=c^16,d^a=d^190,d^b=d^39373 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32470, 12);