Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C7×C11 ⋊ SD16 |
| Sylow | C11 ⋊ #1142 |
| Sylow | C7 ⋊ #4314 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 616 |
Polycyclic presentation:
2^4,7,11|b^2=c,c^2=d,b^a=bc,c^a=cd,f^a=f^10,e^b=e^6122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 16);