Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C4×#88523 |
| Fitting | C3×C4×C8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C4×M16 |
710 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 259 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9814);