Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C3×#10592853 |
| Fitting | C2×C33×D8 ⋊ C2 |
| Sylow | C33 ⋊ #496 |
1168 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 29252);