Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#3701 |
| Fitting | C2×C3×Q8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#41 |
530 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #13140711, #13140731, #13140737, … |
| maximal normal subgroup of | #13140711, #13140731, #13140737, … |
| maximal quotient of | C2×C3×#63452, C2×C3×#63454, C2×C3×#63455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2587);