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×Dic72 |
| Sylow | C3×C9 ⋊ Q32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | #13134897, #13134898, #13134903, … |
| maximal normal subgroup of | #13134897, #13134898, #13134903, … |
| maximal quotient of | C3×#10588181, C3×#10588180, C2×C3×Dic72 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 312);