Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C9×#10625191 |
| Fitting, Hall | C52×C9×C37 ⋊ C4 |
| derived | C5×C37 ⋊ C4×C5×C9 |
| Hall | C52×C37 ⋊ C4×C9 |
| Hall | C9×C37 ⋊ C5×AGL(1,𝔽5) |
| Hall | C52×C9 ⋊ #3866 |
| Sylow | C37 ⋊ C5×C9×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C9×#3866 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6660 |
2250 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 271);