Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C2×C3×C8×#157 |
| Fitting | C2×C33×C8 ⋊ C4 |
| derived | C32 ⋊ C2×C3×C4×C8 |
| Sylow | C33 ⋊ C2×C4×C8 |
520 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, 39297);