Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63545 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#63547 |
| Sylow | C33 ⋊ SD32 |
162 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63547, #13155204, #13155205, … |
| maximal normal subgroup of | D3×#63547, #13155204, #13155205, … |
| maximal quotient of | C3×#10589114, C3×#10589117, C3×#10589142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1930);