Finite Group DatabasebetaFinite Group Databasebeta| order | 31375 |
| automorphism | ? |
| homology | Abelianization (H1) = C125 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C251 ⋊ C125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C25 | C251⋊C5 |
| commutator, hypocenter | C251 | C125 |
| Fitting, cosocle | C25×C251 | C5 |
| socle, prime radical | C5×C251 | C25 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C25 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
5^3,251|a^5=b,b^5=c,d^a=d^2191375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31375, 6);