Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#64110 |
| Fitting | C2×C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ #131 |
460 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589113, #13145559, #13145560, … |
| maximal normal subgroup of | C3×#10589113, #13145559, #13145560, … |
| maximal quotient of | C3×C8×#634, C3×#10592378, C3×C8×C4⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3823);