Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29×C3 |
| direct product | C22×C3×#3828 |
| Fitting | C23×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C22×#41 |
6284 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47796);