Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210×C3 |
| direct product | C23×#638⋊C3 |
| Fitting | C25×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C23×D4 |
5515 conjugacy classes of subgroups; only the 1204 normal subgroups are shown.
This group has 5515 conjugacy classes of subgroups — too many to draw. Only its 1204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 31031);