Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C25×C3 |
| direct product | C3×C3⋊D3×#95 |
| Fitting | C33×#95 ⋊ C2 |
| Sylow | C33 ⋊ C2×#95 |
2284 conjugacy classes of subgroups; only the 470 normal subgroups are shown.
This group has 2284 conjugacy classes of subgroups — too many to draw. Only its 470 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28768);