Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C33 |
| direct product | #95×C3⋊(C3⋊D3) |
| Fitting | C33×#95 ⋊ C2 |
| Sylow | C33 ⋊ C2×#95 |
4620 conjugacy classes of subgroups; only the 807 normal subgroups are shown.
This group has 4620 conjugacy classes of subgroups — too many to draw. Only its 807 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, 29370);