Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×D3×M16 |
| Fitting | C33×M16 ⋊ C2 |
| Sylow | C33 ⋊ C2×M16 |
488 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#822, C3×#10590973, C3×D3×#823, … |
| maximal normal subgroup of | C3×D3×#822, C3×#10590973, C3×D3×#823, … |
| maximal quotient of | C32×#4707, C32×#4701, C32×D3×#97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3742);