Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3×C4 |
| direct product | C9×#127⋊C3 |
| Fitting | C9×#127 ⋊ C3 |
| derived | C42 ⋊ C2×C3×C9 |
| Sylow | #127 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #127⋊C3 |
| commutator, hypocenter | C42 | C2×C3×C9 |
| Frattini, socle | C22×C3 | C2×C3×A4 |
| Fitting | C9×#127 | C3 |
| prime radical | C3×#127⋊C3 | C3 |
| cosocle | C3×C42 | C2×C32 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C9 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#4626, C9⋊#4626, C9×#857⋊C2, … |
| maximal normal subgroup of | C9×#4626, C9⋊#4626, C9×#857⋊C2, … |
| maximal quotient of | C9×#384⋊C3, C9×#392⋊C3, C9×#399⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1301);