Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C3⋊AGL(1,𝔽9) |
| Fitting | C33×C4 ⋊ C8 |
| derived, Sylow | C33 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊AGL(1,𝔽9) |
| commutator, hypocenter | C33 | C4×C8 |
| Frattini | C2 | C2×C3⋊AGL(1,𝔽9) |
| Fitting | C33×C4 | C8 |
| socle | C2×C33 | C2×C8 |
| prime radical | C2×C3×C3⋊D3 | C2×C4 |
| cosocle | C2×C3×#157 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×AGL(1,𝔽9), #13165040, #13165041, … |
| maximal normal subgroup of | C3⋊C8×AGL(1,𝔽9), #13165040, #13165041, … |
| maximal quotient of | C8×C3⋊AGL(1,𝔽9), #13166205, #13166208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4206);