Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#929 |
| Fitting | C22×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ #123 |
684 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10591398, #13160876, C32×#5053, … |
| maximal normal subgroup of | C3×#10591398, #13160876, C32×#5053, … |
| maximal quotient of | C32×#4933, C32×#4940, C32×#4952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3765);