Finite Group DatabasebetaFinite Group Databasebeta| order | 32275 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1291⋊C25 |
| derived, Sylow | C1291 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C1291⋊C5 |
| commutator, hypocenter | C1291 | C25 |
| Fitting, socle, prime radical, cosocle | C5×C1291 | C5 |
| LCS | G ▷ C1291 | |
| UCS | C1 ◁ C5 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32275 |
Polycyclic presentation:
5^2,1291|a^5=b,c^a=c^3441315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32275, 1);