Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
| direct product | Q8×C4⋊(C3⋊(C3⋊D3)) |
| Fitting | C33×C4×Q8 ⋊ C2 |
| Sylow | C33 ⋊ D4×Q8 |
3920 conjugacy classes of subgroups; only the 955 normal subgroups are shown.
This group has 3920 conjugacy classes of subgroups — too many to draw. Only its 955 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45763);