Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4⋊(C3⋊(C3⋊C8)) |
| unambiguous semidirect product | C4⋊(C3×C3⋊(C3⋊C8)) |
| Sylow | C33 ⋊ C4⋊C8 |
348 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2100);