Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C3)⋊Q8 |
| unambiguous semidirect product | Dic98⋊C3 |
| Hall | Dic98 ⋊ C3 |
| Hall | C49⋊C3 ⋊ Q8 |
| Sylow | C49 ⋊ C3×Q8 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
Polycyclic presentation:
2^2,3,2,7^2|a^2=d,b^2=d,e^7=f,b^a=bd,e^a=e^6f^6,f^a=f^6,e^c=e^4f^2,f^c=f^447 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 7);