Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C24 |
| direct product | C2×C9×#1020 |
| Fitting | C25×C9 ⋊ D3 |
| derived | C22⋊A4 ⋊ C22×C9 |
742 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal quotient of | C2×C9×#5935 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46148);