Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic289 |
| unambiguous semidirect product | (C7×Dic289)⋊C3 |
| derived, Hall | C7×C289 ⋊ C3×C4 |
| Hall | C7×Dic289 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C289 ⋊ C4 |
| Sylow | C289 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×Dic289 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8092 |
1460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 2);