Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | Q8×C9×Dic3 |
| Sylow | C3×C9 ⋊ C4×Q8 |
248 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×#3674, #13140653, #13140655, … |
| maximal normal subgroup of | Dic3×#3674, #13140653, #13140655, … |
| maximal quotient of | C9×Dic3×C4⋊C4, C9×#4980, C9×#4984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1629);