Finite Group DatabasebetaFinite Group Databasebeta| order | 30300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C101 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×AGL(1,𝔽5)×C101 |
| Fitting, socle, Hall | C3×C52×C101 ⋊ C4 |
| derived | C5 ⋊ C3×C4×C5×C101 |
| Hall | C52×C101 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ C4×C101 |
| Sylow | C52 ⋊ C3×C4×C101 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6060 |
7575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30300, 139);