Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D867 |
| unambiguous semidirect product | (C3×D7)⋊D289 |
| unambiguous semidirect product | (D7×C289)⋊D3 |
| Fitting, derived, Hall | C3×C7×C289 ⋊ C22 |
| Hall | C7×C289 ⋊ C2×D3 |
| Hall | C3×C289 ⋊ C2×D7 |
| Sylow | C289 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D289 |
| Sylow | C7 ⋊ C2×D867 |
| Sylow | C3 ⋊ D7×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C289 | C22 |
| Frattini | C17 | D7×D51 |
| socle | C3×C7×C17 | C2×D17 |
| LCS | G ▷ C3×C7×C289 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6069 |
2175 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 28);