Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | D3×C22⋊#157 |
| Fitting | C22×C33 ⋊ C2×C4 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
596 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63738, #13165456, D3×#63774, … |
| maximal normal subgroup of | D3×#63738, #13165456, D3×#63774, … |
| maximal quotient of | #13166418, #13166425, D3×#63774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4239);