Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C7 ⋊ SD16 |
| Sylow | C32 ⋊ #1132 |
| Sylow | C7 ⋊ #3715 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^4,3^2,7|b^2=c,c^2=d,b^a=bc,c^a=cd,e^a=e^2,g^a=g^6,e^b=e^2,f^b=f^293 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 392);