Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22×C4 |
| direct product | C9×#940 |
| Fitting | C2×C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #127 |
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | #13135196, C9×#4474, #13140270, … |
| maximal normal subgroup of | #13135196, C9×#4474, #13140270, … |
| maximal quotient of | C9×#4957, C9×#4949, C9×#4960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1599);