Finite Group DatabasebetaFinite Group Databasebeta| order | 19434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊(D79⋊C3) |
| unambiguous semidirect product | (C79⋊C3)⋊D41 |
| unambiguous semidirect product | D3239⋊C3 |
| Fitting, socle, derived, Hall | C41×C79 ⋊ C2×C3 |
| Hall | C41×C79⋊C3 ⋊ C2 |
| Hall | D3239 ⋊ C3 |
| Hall | C79⋊C3 ⋊ D41 |
| Sylow | C79 ⋊ C3×D41 |
| Sylow | C41 ⋊ D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C79 | C2×C3 |
| LCS | G ▷ C41×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3239 |
Polycyclic presentation:
2,3,41,79|c^a=c^40,d^a=d^78,d^b=d^23599 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19434, 12);