Finite Group DatabasebetaFinite Group Databasebeta| order | 17496 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | D32×AGL(1,ℤ/27) |
| Fitting, Sylow | C32×#6875 ⋊ C23 |
| derived | C32×C27 ⋊ C23×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C32×C27 | C23×C9 |
| Frattini | C3×C9 | C3×D33 |
| Fitting | C32×#6875 | C23 |
| socle | C33 | C22×D9⋊C9 |
| prime radical | D32×D27⋊C3 | C3 |
| cosocle | C32×C27⋊C3 | C23×C3 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 | |
1450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
279 conjugacy classes. The character table is too large to display.
| holomorph of | D3×C27 |
Past the SmallGroups library coverage — no SmallGroups id.