Finite Group DatabasebetaFinite Group Databasebeta| order | 8748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C9×#92265⋊C2 |
| Fitting, Sylow | C9×#6900 ⋊ C22 |
| derived | C92 ⋊ C22×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #92265⋊C2 |
| commutator, hypocenter | C92 | C22×C3×C9 |
| Frattini, socle | C33 | C32×D32 |
| Fitting | C9×#6900 | C22 |
| prime radical | C3×#92265⋊C2 | C3 |
| cosocle | C3×C92 | C22×C32 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C9 | |
1028 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | 3−1+2×#92265⋊C2, D9×#92265⋊C2 |
| maximal normal subgroup of | 3−1+2×#92265⋊C2, D9×#92265⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.