Finite Group DatabasebetaFinite Group Databasebeta| order | 23226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D237 |
| unambiguous semidirect product | C3⋊(C49×D79) |
| unambiguous semidirect product | C79⋊(D3×C49) |
| Fitting, Hall | C3×C49×C79 ⋊ C2 |
| derived, Hall | C3×C79 ⋊ C2×C49 |
| Hall | C49×C79 ⋊ D3 |
| Hall | C3×C49 ⋊ D79 |
| Sylow | C79 ⋊ D3×C49 |
| Sylow | C3 ⋊ C49×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D237 |
| commutator, hypocenter | C3×C79 | C2×C49 |
| Frattini | C7 | C7×D237 |
| Fitting | C3×C49×C79 | C2 |
| socle, cosocle | C3×C7×C79 | C2×C7 |
| prime radical | C7×D237 | C7 |
| LCS | G ▷ C3×C79 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11613 |
5880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23226, 10);