Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C32×C7×C8 ⋊ C2 |
| Hall | C32×C7 ⋊ M16 |
| Sylow | C32 ⋊ #1131 |
| Sylow | C7 ⋊ #3743 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^4,3^2,7|b^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^6258 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 475);