Finite Group DatabasebetaFinite Group Databasebeta| order | 32450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C59⋊(D11⋊C25) |
| unambiguous semidirect product | (C11⋊C25)⋊D59 |
| unambiguous semidirect product | D649⋊C25 |
| derived, Hall | C11×C59 ⋊ C2×C25 |
| Hall | C59×C11⋊C25 ⋊ C2 |
| Hall | D649 ⋊ C25 |
| Hall | C11⋊C25 ⋊ D59 |
| Sylow | C59 ⋊ D11⋊C25 |
| Sylow | C11 ⋊ C25×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | (C11⋊C5)⋊D59 |
| commutator, hypocenter | C11×C59 | C2×C25 |
| Fitting, socle, cosocle | C5×C11×C59 | C2×C5 |
| prime radical | C5×D649 | C5 |
| LCS | G ▷ C11×C59 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16225 |
Polycyclic presentation:
2,5,11,59,5|b^5=e,c^a=c^10,d^a=d^58,c^b=c^41070 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32450, 12);