Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | Q8×(C3⋊(C3⋊C8))⋊C3 |
| Sylow | H(3,𝔽3) ⋊ C8×Q8 |
427 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 427 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8851);