Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C7×C9 ⋊ M16 |
| Sylow | C9 ⋊ #1136 |
| Sylow | C7 ⋊ #3667 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^4,3,7,3|a^2=c,c^2=d,e^3=g,b^a=bd,e^a=e^2g^2,f^a=f^6,g^a=g^2258 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 96);