Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #857 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#857 |
| Fitting | C42×C9 ⋊ D3 |
| derived | C42⋊C3 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #857 |
| commutator, hypocenter | C42⋊C3 | C2×C9 |
| Frattini, socle | C22×C3 | C3×S4 |
| Fitting | C42×C9 | D3 |
| prime radical | C3×#857 | C3 |
| cosocle | C3×C42⋊C3 | C2×C3 |
| LCS | G ▷ C42⋊C3 | |
| UCS | C1 ◁ C9 | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 108 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#857, #857⋊D9, C2×C9×#857, … |
| maximal normal subgroup of | D9×#857, #857⋊D9, C2×C9×#857, … |
| maximal quotient of | C9×#4621, C9×#4622, C9×#4623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 680);