Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#63877 |
| Sylow | C33 ⋊ #117 |
410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #13167878, #13167879, #13167884, … |
| maximal normal subgroup of | #13167878, #13167879, #13167884, … |
| maximal quotient of | C3×#10590655, C3×#10590660, C3×#10590696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3169);