Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63653 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×#63656 |
| Sylow | C33 ⋊ Q32 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#829, C3×#10591042, C3×#10591045, … |
| maximal normal subgroup of | C3×D3×#829, C3×#10591042, C3×#10591045, … |
| maximal quotient of | C3×#10589355, C3×#10589358, C3×#10589430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2125);