Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C3 |
| direct product | C41×#11744707 |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C4 |
| derived, Hall | C32×C52 ⋊ C4×C41 |
| Hall | C52×C41 ⋊ #157 |
| Hall | C32×C41 ⋊ #1043 |
| Sylow | C52 ⋊ #157×C41 |
| Sylow | C32 ⋊ C41×#1043 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6150 |
2460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 476);