Finite Group DatabasebetaFinite Group Databasebeta| order | 29505 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C281⋊C7 |
| unambiguous semidirect product | (C5×C281)⋊(C3×C7) |
| unambiguous semidirect product | (C3×C5×C281)⋊C7 |
| Fitting, socle, Hall | C3×C5×C281 ⋊ C7 |
| derived, Sylow | C281 ⋊ C3×C5×C7 |
| Hall | C5×C281 ⋊ C3×C7 |
| Hall | C3×C281 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C281⋊C7 |
| commutator, cosocle, hypocenter | C281 | C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C281 | C7 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4215 |
705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29505, 2);