Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×AGL(1,𝔽9) |
| Fitting | C33×C4 ⋊ C8 |
| derived | C32 ⋊ C3×C4×C8 |
| Sylow | C33 ⋊ C4×C8 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×AGL(1,𝔽9), #13165040, #13165042, … |
| maximal normal subgroup of | C3⋊C8×AGL(1,𝔽9), #13165040, #13165042, … |
| maximal quotient of | C3×C8×AGL(1,𝔽9), C3×#10593251, C3×#10593254, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4199);