Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | D4×Q8⋊C27 |
| unambiguous semidirect product | C4⋊(C2×Q8⋊C27) |
| unambiguous semidirect product | (D4×Q8)⋊C27 |
| Sylow | D4×Q8 ⋊ C27 |
245 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2246);