Finite Group DatabasebetaFinite Group Databasebeta| order | 19630 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊(D151⋊C5) |
| unambiguous semidirect product | (C151⋊C5)⋊D13 |
| unambiguous semidirect product | D1963⋊C5 |
| Fitting, socle, derived, Hall | C13×C151 ⋊ C2×C5 |
| Hall | C13×C151⋊C5 ⋊ C2 |
| Hall | D1963 ⋊ C5 |
| Hall | C151⋊C5 ⋊ D13 |
| Sylow | C151 ⋊ C5×D13 |
| Sylow | C13 ⋊ D151⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C151 | C2×C5 |
| LCS | G ▷ C13×C151 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1963 |
Polycyclic presentation:
2,5,13,151|c^a=c^12,d^a=d^150,d^b=d^59235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19630, 12);