Finite Group DatabasebetaFinite Group Databasebeta| order | 24966 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×#4294⋊C2 |
| unambiguous semidirect product | #4294⋊(C2×C73) |
| derived, Sylow | C19 ⋊ C2×C9×C73 |
| Hall | C73×#4294 ⋊ C2 |
| Hall | D19×C73 ⋊ C9 |
| Hall | C19×C73 ⋊ C2×C9 |
| Hall | #4294 ⋊ C2×C73 |
| Hall | D19 ⋊ C9×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C73 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C9×C73 |
| Frattini | C3 | C73×D19⋊C3 |
| Fitting, socle | C3×C19×C73 | C2×C3 |
| prime radical | C3×D19×C73 | C3 |
| cosocle | C3×C19 | C2×C3×C73 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C73 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12483 |
1971 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24966, 18);