Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C3 |
| direct product | C23×C4⋊(C3⋊D9) |
| Fitting | C23×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C23×D4 |
6810 conjugacy classes of subgroups; only the 1487 normal subgroups are shown.
This group has 6810 conjugacy classes of subgroups — too many to draw. Only its 1487 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 31036);