Finite Group DatabasebetaFinite Group Databasebeta| order | 34650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5775 |
| unambiguous semidirect product | C7⋊(C3⋊D825) |
| unambiguous semidirect product | C11⋊(C3⋊D525) |
| unambiguous semidirect product | C25⋊(C3⋊D231) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C7×C11×C25 | C2 |
| Frattini | C5 | C3⋊D1155 |
| socle | C32×C5×C7×C11 | D5 |
| LCS | G ▷ C32×C7×C11×C25 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17325 |
Polycyclic presentation:
2,3^2,5,7,11,5|d^5=g^4,b^a=b^2,c^a=c^2,d^a=d^4g,e^a=e^6,f^a=f^10,g^a=g^48664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34650, 96);