Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#63771 |
| Sylow | C33 ⋊ #108 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #13154739, #13154740, #13154755, … |
| maximal normal subgroup of | #13154739, #13154740, #13154755, … |
| maximal quotient of | C3×#10590172, C3×#10590171, C3×#10590185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3038);