Finite Group DatabasebetaFinite Group Databasebeta| order | 31375 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C251 · Schur multiplier (H2) = C1 |
| direct product | 5−1+2×C251 |
| unambiguous semidirect product | C25⋊(C5×C251) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C5×C251 | C52 |
| commutator, Frattini, cosocle | C5 | C52×C251 |
| prime radical | C52×C251 | C5 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C251 ◁ G | |
20 conjugacy classes of subgroups.
7279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31375, 4);