Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊#63422 |
| unambiguous semidirect product | (C2×C3)⋊#63422 |
| derived | C3×Q8⋊C9 ⋊ C2×C4 |
448 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13147076, C2×#72252951 |
| maximal normal subgroup of | C2×#13147076, C2×#72252951 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13126);