Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2 |
| direct product | C3×#63555 |
| Sylow | C33 ⋊ #97 |
250 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590035, C3×#10590036, #13154974, … |
| maximal normal subgroup of | C3×#10590035, C3×#10590036, #13154974, … |
| maximal quotient of | C3×#10589078, C3×#10589106, C3×#10589156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1938);