Finite Group DatabasebetaFinite Group Databasebeta| order | 31575 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C421⋊C3)⋊C25 |
| unambiguous semidirect product | (C421⋊C25)⋊C3 |
| derived, Sylow | C421 ⋊ C3×C25 |
| Hall | C421⋊C25 ⋊ C3 |
| Hall | C421⋊C3 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | (C421⋊C3)⋊C5 |
| commutator, hypocenter | C421 | C3×C25 |
| Fitting, socle, cosocle | C5×C421 | C3×C5 |
| prime radical | C5×C421⋊C3 | C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10525 |
Polycyclic presentation:
3,5,421,5|b^5=d,c^a=c^400,c^b=c^279215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31575, 2);