Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×#63386⋊C3 |
| unambiguous semidirect product | (C2×#63386)⋊C3 |
| Sylow | 3−1+2 ⋊ C2×SD32 |
308 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9378);