Finite Group DatabasebetaFinite Group Databasebeta| order | 31575 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C421⋊C3 |
| unambiguous semidirect product | (C25×C421)⋊C3 |
| Fitting, Hall | C25×C421 ⋊ C3 |
| derived, Sylow | C421 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C421⋊C3 |
| commutator, hypocenter | C421 | C3×C25 |
| Frattini | C5 | C5×C421⋊C3 |
| Fitting | C25×C421 | C3 |
| socle, cosocle | C5×C421 | C3×C5 |
| prime radical | C5×C421⋊C3 | C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10525 |
3575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31575, 4);