Finite Group DatabasebetaFinite Group Databasebeta| order | 8748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C9 |
| direct product | AGL(1,ℤ/9)×C9⋊D9 |
| Fitting, Sylow | C92×3−1+2 ⋊ C22 |
| derived | C93 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C93 | C22×C3 |
| Frattini, socle | C33 | C3×D3×C3⋊D3 |
| Fitting | C92×3−1+2 | C22 |
| LCS | G ▷ C93 | |
| UCS | C1 | |
1580 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/9)×#92314, D92×AGL(1,ℤ/9) |
| maximal normal subgroup of | AGL(1,ℤ/9)×#92314, D92×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.