Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C3×#64084 |
| Fitting | C33×C42 ⋊ C2 |
| Sylow | C33 ⋊ #124 |
576 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589087, #13145519, #13145702, … |
| maximal normal subgroup of | C3×#10589087, #13145519, #13145702, … |
| maximal quotient of | C3×#10592372, C3×#10592358, C3×#10592371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3797);