Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×C4⋊(D9⋊A4) |
| unambiguous semidirect product | (C2×D36)⋊A4 |
| Fitting | C23×C4×C9 ⋊ C2×C3 |
967 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 967 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) = 216 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30629);