Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #4245 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#4245 |
| Hall | C3×C7×C9 ⋊ D4 |
| Sylow | C3×C9 ⋊ C22⋊D7 |
| Sylow | C7 ⋊ C9×#67 |
116 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 233);