Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#63886 |
| Sylow | C33 ⋊ #121 |
506 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #13167920, #13167982, #13168053, … |
| maximal normal subgroup of | #13167920, #13167982, #13168053, … |
| maximal quotient of | C3×#10590576, C3×#10590577, C3×#10590585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3178);