Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#63737 |
| Sylow | C33 ⋊ #95 |
292 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593165, #13165100, D3×#63737, … |
| maximal normal subgroup of | C3×#10593165, #13165100, D3×#63737, … |
| maximal quotient of | C3×#10590043, C3×#10590044, C3×#10590045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2711);