Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C16 · Schur multiplier (H2) = C3×C4 |
| direct product | C3×#10590174 |
| derived | C32 ⋊ C3×C4×C16 |
| Sylow | C33 ⋊ C4×C16 |
248 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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, 23162);