Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C289 · Schur multiplier (H2) = C2 |
| direct product | C22×ΓL(1,𝔽8)×C289 |
| Fitting, Hall | C22×C7×C289 ⋊ C3 |
| derived, Sylow | C7 ⋊ C22×C3×C289 |
| Hall | C7×C289 ⋊ C22×C3 |
| Hall | C22×C7 ⋊ C3×C289 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8092 |
5780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 31);