Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#932 |
| Fitting | C2×C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ AGL(1,ℤ/8) |
624 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10591505, C3×#10591508, C3×#10591506, … |
| maximal normal subgroup of | C3×#10591505, C3×#10591508, C3×#10591506, … |
| maximal quotient of | C32×#4970, C32×#4964, C32×#4966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3768);