Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C3×#64361 |
| Fitting | C2×C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ H(5,𝔽2) |
1212 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 306 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10591532, C3×#10591535, C3×#10591511, … |
| maximal normal subgroup of | C3×#10591532, C3×#10591535, C3×#10591511, … |
| maximal quotient of | C3×#10595954, C3×#10595957, C3×#10595961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4631);