Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C22⋊C8×#272 |
| Fitting | H(3,𝔽3)×C22⋊C8 ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×C22⋊C8 |
1111 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 1111 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9912);