Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C4 |
| direct product | C22×C9⋊(C42⋊C3) |
| Fitting | C22×C42×C9 ⋊ C3 |
| Sylow | C22×C42 ⋊ 3−1+2 |
354 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18164);