Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#63880 |
| Sylow | C33 ⋊ C4×D4 |
490 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #13167905, #13167915, #13167917, … |
| maximal normal subgroup of | #13167905, #13167915, #13167917, … |
| maximal quotient of | C3×#10590341, C3×#10590342, C3×#10590721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3172);