Finite Group DatabasebetaFinite Group Databasebeta| order | 29725 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C41⋊C25 |
| unambiguous semidirect product | C41⋊(C25×C29) |
| unambiguous semidirect product | (C29×C41)⋊C25 |
| derived, Sylow | C41 ⋊ C25×C29 |
| Hall | C29×C41 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C29 | C41⋊C5 |
| commutator, hypocenter | C41 | C25×C29 |
| Frattini | C5 | C29×C41⋊C5 |
| Fitting, socle, prime radical | C5×C29×C41 | C5 |
| cosocle | C5×C41 | C5×C29 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C5×C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 29725 |
1885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29725, 2);