Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×Dic49 |
| unambiguous semidirect product | C49⋊(C4×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×Dic49)⋊C5 |
| derived, Hall | C31×C49 ⋊ C4×C5 |
| Hall | C49×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C31×Dic49 ⋊ C5 |
| Sylow | C49 ⋊ C4×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×Dic49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6076 |
572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 11);