Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#64289 |
| Sylow | C33 ⋊ #131 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593271, #13166225, #13166563, … |
| maximal normal subgroup of | C3×#10593271, #13166225, #13166563, … |
| maximal quotient of | C3×#10593748, C3×#10593749, C3×#10593751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4471);