Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #66561 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#66561 |
| Hall | C32×C7 ⋊ D8 |
| Sylow | C32 ⋊ D56 |
| Sylow | C7 ⋊ C3×#213 |
104 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72245820, C3×D7×#213, #72245827, … |
| maximal normal subgroup of | #72245820, C3×D7×#213, #72245827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 300);