Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C33 |
| direct product | C2×#11722198 |
| Fitting | C2×C33×Q16 ⋊ C2 |
| Sylow | C33 ⋊ C2×SD32 |
1260 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 403 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 29888);