Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×#803 |
| Sylow | C33 ⋊ C2×#97 |
1036 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#97, C3⋊D3×#5014 |
| maximal normal subgroup of | D3×C3⋊D3×#97, C3⋊D3×#5014 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24971);