Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#638⋊A4 |
| unambiguous semidirect product | (C2×#638)⋊A4 |
| Fitting | C25×C32 ⋊ C2×C3 |
1696 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 1696 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30707);