Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2 |
| direct product | M16×C22⋊C27 |
| unambiguous semidirect product | (C22×M16)⋊C27 |
| Sylow | C22×M16 ⋊ C27 |
209 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2253);