Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊(C3⋊S4) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C33 |
| direct product | C2×C4×C3⋊(C3⋊S4) |
| Fitting | C23×C32×C4 ⋊ D3 |
| derived | C32×A4 ⋊ C22×C4 |
2262 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2262 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47457);