Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210×C3 |
| direct product | C23×C3×C4⋊(C3⋊D3) |
| Fitting | C23×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C23×D4 |
9116 conjugacy classes of subgroups; only the 2030 normal subgroups are shown.
This group has 9116 conjugacy classes of subgroups — too many to draw. Only its 2030 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47795);