Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#876 |
| Fitting | C3×C42×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #126 |
210 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13147506, #13147512, #13147526, … |
| maximal normal subgroup of | #13147506, #13147512, #13147526, … |
| maximal quotient of | C9×#4658, C9×#4676, C9×C3⋊#401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1345);