Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#64225 |
| Sylow | C33 ⋊ C2×D8 |
292 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593160, #13165095, #13165193, … |
| maximal normal subgroup of | C3×#10593160, #13165095, #13165193, … |
| maximal quotient of | C3×#10593275, C3×#10593277, C3×#10593276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4247);