Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #126⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C22 |
| direct product | C2×#126⋊C27 |
| unambiguous semidirect product | (C2×#126)⋊C27 |
| derived | C42 ⋊ C22×C27 |
| Sylow | C2×#126 ⋊ C27 |
168 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2243);