Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | C3⋊D3×#215 |
| Fitting | C33×Q8 ⋊ C22 |
| Sylow | C33 ⋊ C2×SD16 |
488 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #157×#215, #13166556, #13166557, … |
| maximal normal subgroup of | #157×#215, #13166556, #13166557, … |
| maximal quotient of | #13159076, #13159101, #13159102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3536);