Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C7×C9 ⋊ SD16 |
| Sylow | C9 ⋊ #1143 |
| Sylow | C7 ⋊ #3664 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^4,3,7,3|a^2=c,b^2=d,c^2=d,e^3=g,b^a=bcd,f^a=f^6,c^b=cd,e^b=e^2g^2,g^b=g^2102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 28);