Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#822 |
| Sylow | C33 ⋊ #108 |
260 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 114 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 | C3×D3×#822, C3×#10590972, C3×#10590973, … |
| maximal normal subgroup of | C3×D3×#822, C3×#10590972, C3×#10590973, … |
| maximal quotient of | C32×#4479, C32×#4480, C32×#4558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2077);