Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #4179 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#10619505 |
| derived | C3×C9 ⋊ C2×C3×C8 |
| Sylow | #732 ⋊ C2×C8 |
134 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 371);