Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C32 · Schur multiplier (H2) = C210×C3 |
| direct product | C23×C32×D12 |
| Fitting | C23×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C23×D4 |
9116 conjugacy classes of subgroups; only the 3258 normal subgroups are shown.
This group has 9116 conjugacy classes of subgroups — too many to draw. Only its 3258 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47775);