Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C3×#64083 |
| Fitting | C33×C42 ⋊ C2 |
| Sylow | C33 ⋊ #127 |
768 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589091, #13145525, #13145704, … |
| maximal normal subgroup of | C3×#10589091, #13145525, #13145704, … |
| maximal quotient of | C3×#10592370, C3×#10592376, C3×#10592392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3796);