Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C49⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C49⋊(AGL(1,𝔽5)×C31) |
| Fitting, Hall | C5×C31×C49 ⋊ C4 |
| derived, Hall | C5×C49 ⋊ C4×C31 |
| Hall | C31×C49 ⋊ AGL(1,𝔽5) |
| Hall | C5×C31 ⋊ Dic49 |
| Sylow | C49 ⋊ AGL(1,𝔽5)×C31 |
| Sylow | C5 ⋊ C31×Dic49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7595 |
3131 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 22);