Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×Dic3×D12 |
| Sylow | C33 ⋊ C4×D4 |
502 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#3713, Dic3×#3714, #13155614, … |
| maximal normal subgroup of | Dic3×#3713, Dic3×#3714, #13155614, … |
| maximal quotient of | C3×C3⋊C8×D12, C3×#10590326, C3×#10590337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3184);