Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C22×C3×#3802 |
| Fitting | C22×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ C23×D4 |
6210 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47602);