Finite Group DatabasebetaFinite Group Databasebeta| order | 32630 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊(D251⋊C5) |
| unambiguous semidirect product | (C251⋊C5)⋊D13 |
| unambiguous semidirect product | D3263⋊C5 |
| Fitting, socle, derived, Hall | C13×C251 ⋊ C2×C5 |
| Hall | C13×C251⋊C5 ⋊ C2 |
| Hall | D3263 ⋊ C5 |
| Hall | C251⋊C5 ⋊ D13 |
| Sylow | C251 ⋊ C5×D13 |
| Sylow | C13 ⋊ D251⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C251 | C2×C5 |
| LCS | G ▷ C13×C251 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3263 |
Polycyclic presentation:
2,5,13,251|c^a=c^12,d^a=d^250,d^b=d^219365 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32630, 12);