Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×#64162 |
| Fitting | C24×C33 ⋊ C2 |
| Sylow | C33 ⋊ #120 |
1316 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1316 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590223, #13157240, C3×#10591725, … |
| maximal normal subgroup of | C3×#10590223, #13157240, C3×#10591725, … |
| maximal quotient of | C3×#10592909, C3×#10592912, C3×#10592917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3875);