Finite Group DatabasebetaFinite Group Databasebeta| order | 30900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊(C103⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C3⋊(C5×C103⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C103⋊(C5×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C3×C52×C103 ⋊ C4 |
| derived | C3×C5×C103 ⋊ C4×C5 |
| Hall | C52×C103 ⋊ Dic3 |
| Hall | C3×C103 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C103 ⋊ C5×ΓL(1,𝔽16) |
| Hall | C3×C52 ⋊ Dic103 |
| Sylow | C52 ⋊ Dic309 |
| Sylow | C3 ⋊ C5×C103⋊AGL(1,𝔽5) |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6180 |
3105 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30900, 128);