Finite Group DatabasebetaFinite Group Databasebeta| order | 30300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C3⋊#87938 |
| unambiguous semidirect product | C3⋊(C25×#87938) |
| Fitting, Hall | C3×C25×C101 ⋊ C4 |
| derived, Hall | C3×C101 ⋊ C4×C25 |
| Hall | C25×C101 ⋊ Dic3 |
| Sylow | C101 ⋊ Dic3×C25 |
| Hall | C3×C25 ⋊ #87938 |
| Sylow | C3 ⋊ C25×#87938 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7575 |
2025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30300, 29);