Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | Dic3×#634 |
| Sylow | C33 ⋊ C4×Q8 |
524 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 156 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 | Dic3×#3716, #13155640, Dic3×#3719, … |
| maximal normal subgroup of | Dic3×#3716, #13155640, Dic3×#3719, … |
| maximal quotient of | C3⋊C8×#634, #13158783, #13158868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3365);