Finite Group DatabasebetaFinite Group Databasebeta| order | 1632 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C17 ⋊ C22⋊Q8 |
| Sylow | C17 ⋊ #896 |
| Sylow | C3 ⋊ #10587564 |
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 816 |
Polycyclic presentation:
2^5,3,17|a^2=e,c^2=e,c^a=cd,g^a=g^16,c^b=cde,f^b=f^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1632, 479);