Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C3×#64145 |
| Sylow | C33 ⋊ #124 |
672 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589181, #13145682, #13145742, … |
| maximal normal subgroup of | C3×#10589181, #13145682, #13145742, … |
| maximal quotient of | C3×#10592644, C3×#10592646, C3×#10592652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3858);