Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#64155 |
| Fitting | C2×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ C22⋊Q8 |
596 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590215, #13157232, C3×#10591553, … |
| maximal normal subgroup of | C3×#10590215, #13157232, C3×#10591553, … |
| maximal quotient of | C3×#10592677, C3×#10592671, C3×#10592692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3868);