Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D9×Dic3⋊C4 |
| Sylow | C3×C9 ⋊ C2×C4⋊C4 |
302 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D9×Dic6, #13147477, #13147479, … |
| maximal normal subgroup of | C4×D9×Dic6, #13147477, #13147479, … |
| maximal quotient of | D9×#807, #13137614, D9×#808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 940);