Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #88543 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C4×#88544 |
| Fitting | C3×C4×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C4×D8 |
670 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 10470);