Finite Group DatabasebetaFinite Group Databasebeta| order | 30900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×(C103⋊C3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C103⋊C3)⋊(C5×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C103⋊AGL(1,𝔽5))⋊(C3×C5) |
| unambiguous semidirect product | (C5×C103⋊AGL(1,𝔽5))⋊C3 |
| Fitting, socle, Hall | C52×C103 ⋊ C3×C4 |
| derived | C5×C103 ⋊ C3×C4×C5 |
| Hall | C5×C103⋊AGL(1,𝔽5) ⋊ C3 |
| Hall | C52×C103⋊C3 ⋊ C4 |
| Hall | C103⋊C3 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C103 ⋊ C3×C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ (C103⋊C3)⋊C4 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2060 |
415 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30900, 83);