Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#834 |
| Sylow | C33 ⋊ #99 |
528 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589172, C3×#10589174, C3×#10589175, … |
| maximal normal subgroup of | C3×#10589172, C3×#10589174, C3×#10589175, … |
| maximal quotient of | C32×#4525, C32×#4526, C32×#4528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2089);