Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#876 |
| Fitting | C33×C42 ⋊ C2 |
| Sylow | C33 ⋊ #126 |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10593914, C3×#10593919, C3×#10593928, … |
| maximal normal subgroup of | C3×#10593914, C3×#10593919, C3×#10593928, … |
| maximal quotient of | C32×#4658, C32×#4676, C32×C3⋊#401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3712);