Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#63907 |
| Sylow | C33 ⋊ #124 |
426 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 96 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 | #13167933, #13167937, #13167941, … |
| maximal normal subgroup of | #13167933, #13167937, #13167941, … |
| maximal quotient of | C3×#10590531, C3×#10590533, C3×#10590535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3199);