Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #126⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#126⋊C9 |
| unambiguous semidirect product | (C3×#126)⋊C9 |
| derived | C42 ⋊ C2×C3×C9 |
| Sylow | #126 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #126⋊C3 |
| commutator, hypocenter | C42 | C2×C3×C9 |
| Frattini | C22×C3 | C2×C3×A4 |
| Fitting | C32×#126 | C3 |
| socle | C22×C32 | C2×A4 |
| prime radical | C23×C32 | A4 |
| cosocle | C3×C42 | C2×C32 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C32 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#126⋊C9, #5711⋊C9, C2×C3×#126⋊C9, … |
| maximal normal subgroup of | D3×#126⋊C9, #5711⋊C9, C2×C3×#126⋊C9, … |
| maximal quotient of | C3×#383⋊C9, C3×#396⋊C9, C3×#401⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1316);