Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#10591532 |
| Sylow | C33 ⋊ B(4,𝔽2) |
1194 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#5032, #72258283, #72258299 |
| maximal normal subgroup of | C3×D3×#5032, #72258283, #72258299 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24519);