Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#64120 |
| Fitting | C33×D8 ⋊ C2 |
| Sylow | C33 ⋊ AGL(1,ℤ/8) |
496 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#911, C3×#10594729, C3×#10594732, … |
| maximal normal subgroup of | C3×D3×#911, C3×#10594729, C3×#10594732, … |
| maximal quotient of | C3×#10592460, C3×#10592461, C3×#10592462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3833);