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×#638 |
| Fitting | C25×C33 ⋊ C2 |
| Sylow | C33 ⋊ C23×D4 |
11164 conjugacy classes of subgroups; only the 2030 normal subgroups are shown.
This group has 11164 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) = 288 |
504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3×#64162, C23×C3⋊(((C22⋊C9)⋊C2)⋊C3) |
| maximal normal subgroup of | C22×C3×#64162 |
| maximal quotient of | C22×C3×#64162 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47812);