Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C9×#874 |
| Fitting | C2×C3×C42×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#127 |
1602 conjugacy classes of subgroups; only the 477 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 477 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18355);