Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C33 |
| direct product | M16×C3⋊(C3⋊D3) |
| Fitting | C33×M16 ⋊ C2 |
| Sylow | C33 ⋊ C2×M16 |
952 conjugacy classes of subgroups; only the 273 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 273 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13160107, #13160110, #13160161, … |
| maximal normal subgroup of | #13160107, #13160110, #13160161, … |
| maximal quotient of | #13163341, #13163342, #97×C3⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3914);