Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #117×D27 |
| Fitting | C27×#117 ⋊ C2 |
| Sylow | C27 ⋊ C2×#117 |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2324);