Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#5838⋊C3 |
| unambiguous semidirect product | #5838⋊C32 |
| unambiguous semidirect product | (C3×#5838)⋊C3 |
| Fitting | C32×2−1+4 ⋊ C2×C3 |
492 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39197);