Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#829 |
| Sylow | C3×C9 ⋊ Q32 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#829, #13139270, #13139271, … |
| maximal normal subgroup of | D9×#829, #13139270, #13139271, … |
| maximal quotient of | C9×#4489, C9×#4492, C9×#4564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 435);