Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×C22⋊PSU(3,𝔽2) |
| Fitting | C22×C33 ⋊ Q8 |
| Sylow | C33 ⋊ C22⋊Q8 |
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593165, #13165118, C3×#10596415, … |
| maximal normal subgroup of | C3×#10593165, #13165118, C3×#10596415, … |
| maximal quotient of | C3×#10593550, C3×#10593548, C3×#10593552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4327);