Finite Group DatabasebetaFinite Group Databasebeta| order | 24966 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D4161 |
| unambiguous semidirect product | C19⋊(C3⋊D219) |
| unambiguous semidirect product | C73⋊(C3⋊D57) |
| Fitting, socle, derived, Hall | C32×C19×C73 ⋊ C2 |
| Hall | C19×C73 ⋊ C3⋊D3 |
| Hall | C32×C73 ⋊ D19 |
| Hall | C32×C19 ⋊ D73 |
| Sylow | C73 ⋊ C3⋊D57 |
| Sylow | C19 ⋊ C3⋊D219 |
| Sylow | C32 ⋊ D1387 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C19×C73 | C2 |
| LCS | G ▷ C32×C19×C73 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12483 |
Polycyclic presentation:
2,3^2,19,73|b^a=b^2,c^a=c^2,d^a=d^18,e^a=e^726243 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24966, 120);