Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C4⋊((C3⋊D3)⋊A4) |
| unambiguous semidirect product | (C2×C4⋊(C3⋊D3))⋊A4 |
| Fitting | C23×C32×C4 ⋊ C2×C3 |
1664 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 1664 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, 30672);