Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×C3⋊#1043 |
| unambiguous semidirect product | C3⋊(#1043×C121) |
| Fitting, Hall | C3×C52×C121 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C4×C121 |
| Hall | C52×C121 ⋊ Dic3 |
| Hall | C3×C121 ⋊ #1043 |
| Sylow | C52 ⋊ Dic3×C121 |
| Sylow | C3 ⋊ #1043×C121 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
2904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 121);