Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C32×D3×C4⋊C4 |
| Fitting | C33×C4⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ C2×C4⋊C4 |
656 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 294 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 | C3×#10590498, C3×#10590422, C3×#10590500, … |
| maximal normal subgroup of | C3×#10590498, C3×#10590422, C3×#10590500, … |
| maximal quotient of | C32×#4667, C32×#4649, C32×#4650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3727);