Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#63359 |
| Fitting | C3×C9×C16 ⋊ C2 |
| Sylow | C3×C9 ⋊ SD32 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63359, #13136968, #13136970, … |
| maximal normal subgroup of | D3×#63359, #13136968, #13136970, … |
| maximal quotient of | C3×#10588182, C3×#10588186, C3×#10588180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 311);