Finite Group DatabasebetaFinite Group Databasebeta| order | 23226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D147 |
| unambiguous semidirect product | C3⋊(C79×D49) |
| unambiguous semidirect product | C49⋊(D3×C79) |
| Fitting, Hall | C3×C49×C79 ⋊ C2 |
| derived, Hall | C3×C49 ⋊ C2×C79 |
| Hall | C49×C79 ⋊ D3 |
| Hall | C3×C79 ⋊ D49 |
| Sylow | C49 ⋊ D3×C79 |
| Sylow | C3 ⋊ C79×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D147 |
| commutator, cosocle, hypocenter | C3×C49 | C2×C79 |
| Frattini | C7 | D21×C79 |
| Fitting | C3×C49×C79 | C2 |
| socle | C3×C7×C79 | D7 |
| LCS | G ▷ C3×C49 | |
| UCS | C1 ◁ C79 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11613 |
5925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23226, 11);