Finite Group DatabasebetaFinite Group Databasebeta| order | 31375 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C25 · Schur multiplier (H2) = C5 |
| direct product | C5×#20262474 |
| unambiguous semidirect product | (C251⋊C5)⋊C25 |
| Fitting, socle | C5×C251 ⋊ C25 |
| derived, Sylow | C251 ⋊ C5×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20262474 |
| commutator, hypocenter | C251 | C5×C25 |
| Frattini | C1 | G |
| Fitting, socle | C5×C251 | C25 |
| prime radical | C5×C251⋊C5 | C5 |
| cosocle | C251⋊C5 | C52 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C5 | |
28 conjugacy classes of subgroups.
175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31375, 17);