Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C3×C4 |
| direct product | C3⋊C8×#157 |
| derived, Sylow | C33 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×#157 |
| commutator, hypocenter | C33 | C4×C8 |
| Fitting | C33×C4 | C2×C4 |
| socle | C2×C33 | C42 |
| prime radical | C2×C3×C3⋊D3 | C2×C4 |
| cosocle | C3×C4×C3⋊D3 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×AGL(1,𝔽9), #13165040, #13165045, … |
| maximal normal subgroup of | C3⋊C8×AGL(1,𝔽9), #13165040, #13165045, … |
| maximal quotient of | #157×C3⋊C16, #13154731, C3⋊C8×#622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2669);