Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C33 |
| direct product | #131×C3⋊(C3⋊D3) |
| Fitting | C33×#131 ⋊ C2 |
| Sylow | C33 ⋊ C2×#131 |
3724 conjugacy classes of subgroups; only the 877 normal subgroups are shown.
This group has 3724 conjugacy classes of subgroups — too many to draw. Only its 877 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45937);