Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C121 · Schur multiplier (H2) = C2 |
| direct product | C2×C121×D75 |
| unambiguous semidirect product | (C2×C3)⋊(D25×C121) |
| unambiguous semidirect product | (C2×C25)⋊(D3×C121) |
| Fitting | C2×C3×C25×C121 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C22×C121 |
| Hall | C3×C25×C121 ⋊ C22 |
| Hall | C25×C121 ⋊ C2×D3 |
| Hall | C3×C121 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D3×C121 |
| Sylow | C3 ⋊ C2×D25×C121 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18150 |
9438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 37);