Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | D3×#3752 |
| Fitting | C2×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
928 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63848, D3×#63868, #13168760, … |
| maximal normal subgroup of | D3×#63848, D3×#63868, #13168760, … |
| maximal quotient of | D3×#63632, #13159048, D3×#63633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3504);