Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×AGL(1,𝔽9) |
| Fitting, socle | C22×C33 ⋊ C8 |
| derived | C32 ⋊ C22×C3×C8 |
| Sylow | C33 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C22×C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33 | C8 |
| prime radical | C22×C3×C3⋊D3 | C4 |
| cosocle | #157 | C23×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C3 | |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #13165061, C3×#10593166, #13165137, … |
| maximal normal subgroup of | #13165061, C3×#10593166, #13165137, … |
| maximal quotient of | C2×C3×#64213, C2×C3×#64214, C3×#10596481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4696);