Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C9 · Schur multiplier (H2) = C210 |
| direct product | C24×D3×C9 |
| unambiguous semidirect product | C3⋊(C25×C9) |
| unambiguous semidirect product | (C2×C3)⋊(C24×C9) |
| Fitting | C24×C3×C9 ⋊ C2 |
| derived | C3 ⋊ C25×C9 |
| Sylow | C3×C9 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C9 | D3 |
| commutator, hypocenter | C3 | C25×C9 |
| Frattini | C3 | C24×C3×D3 |
| Fitting | C24×C3×C9 | C2 |
| socle | C24×C32 | C2×C3 |
| prime radical | C24×C3×D3 | C3 |
| cosocle | C32 | C25×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C24×C9 | |
2378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13141132, C9×#4955, C22×(C2×D3)⋊Dic9, … |
| maximal normal subgroup of | #13141132, C9×#4955, C22×(C2×D3)⋊Dic9, … |
| maximal quotient of | C23×C9×Dic6, C23×C4×D3×C9, C23×C9×D12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4045);