Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C32×#885 |
| Fitting | C33×C22⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ #124 |
592 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#885, C3×#10594270, C3×#10594057, … |
| maximal normal subgroup of | C3×D3×#885, C3×#10594270, C3×#10594057, … |
| maximal quotient of | C32×#4646, C32×#4650, C32×#4673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3721);