Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊Dic289 |
| unambiguous semidirect product | Dic2023⋊C3 |
| derived, Hall | C7×C289 ⋊ C3×C4 |
| Hall | Dic2023 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C289 ⋊ C4 |
| Sylow | C289 ⋊ ΓL(1,𝔽8)⋊C4 |
| Hall | ΓL(1,𝔽8) ⋊ Dic289 |
| Sylow | C7 ⋊ C3×Dic289 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8092 |
Polycyclic presentation:
2,3,7,17,2,17|a^2=e,d^17=f^16,c^a=c^6,d^a=d^16f,f^a=f^16,c^b=c^21454 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 4);