Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | D4×#6204 |
| unambiguous semidirect product | C4⋊(C2×#6204) |
| Sylow | D4×Q8 ⋊ 3−1+2 |
490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18257);