Finite Group DatabasebetaFinite Group Databasebeta| order | 32550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊#13049954 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C25×C31 | C2×C3 |
| Frattini | C5 | C5⋊#13049954 |
| socle | C5×C7×C31 | C3×D5 |
| LCS | G ▷ C7×C25×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5425 |
Polycyclic presentation:
2,3,5,7,31,5|c^5=f^4,c^a=c^4f,e^a=e^30,f^a=f^4,d^b=d^2,e^b=e^5945 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32550, 52);