Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C33 |
| direct product | C2×#11724684 |
| Fitting | C2×C33×#41 ⋊ C2 |
| Sylow | C33 ⋊ C2×H(5,𝔽2) |
12572 conjugacy classes of subgroups; only the 2267 normal subgroups are shown.
This group has 12572 conjugacy classes of subgroups — too many to draw. Only its 2267 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47824);