Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(D7⋊C27) |
| unambiguous semidirect product | D28⋊C27 |
| Hall | C7⋊C27 ⋊ D4 |
| Hall | D28 ⋊ C27 |
| Sylow | C7 ⋊ D4×C27 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 756 |
Polycyclic presentation:
2^2,3,2,3^2,7|b^2=d,c^3=e,e^3=f,b^a=bd,g^a=g^6,g^c=g^4171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 9);