Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#63728 |
| Sylow | C33 ⋊ #101 |
154 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63728, #13165149, #13165152, … |
| maximal normal subgroup of | D3×#63728, #13165149, #13165152, … |
| maximal quotient of | C3×#10590028, C3×#10590036, C3×#10590038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2702);