Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#63788 |
| Sylow | C33 ⋊ #100 |
264 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | #13154855, #13154857, #13154859, … |
| maximal normal subgroup of | #13154855, #13154857, #13154859, … |
| maximal quotient of | C3×#10590204, C3×#10590208, C3×#10590210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3055);