Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C32×C4 |
| direct product | C4×C32⋊(C42⋊C3) |
| unambiguous semidirect product | (C32×C4)⋊(C42⋊C3) |
| unambiguous semidirect product | C43⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C4×C42⋊C3)⋊C3 |
| Fitting | C32×C43 ⋊ C3 |
| Sylow | C43 ⋊ H(3,𝔽3) |
339 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7282);