Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×Dic9 |
| Sylow | C3×C9 ⋊ C4×Q8 |
248 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #13140687, #13140689, #13140693, … |
| maximal normal subgroup of | #13140687, #13140689, #13140693, … |
| maximal quotient of | C3×C4⋊C4×Dic9, C3×#10588660, C3×#10588664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1627);