Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Dic3×Dic18 |
| Sylow | C3×C9 ⋊ C4×Q8 |
236 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #13137477, #13137479, #13137481, … |
| maximal normal subgroup of | #13137477, #13137479, #13137481, … |
| maximal quotient of | C3⋊C8×Dic18, #13137061, #13137069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 875);