Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C33 |
| direct product | C22×Q8×C3⋊(C3⋊D3) |
| Fitting | C22×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ C23×Q8 |
11900 conjugacy classes of subgroups; only the 2531 normal subgroups are shown.
This group has 11900 conjugacy classes of subgroups — too many to draw. Only its 2531 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47820);