Finite Group DatabasebetaFinite Group Databasebeta| order | 31375 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C25×C251 ⋊ C5 |
| Sylow | C251 ⋊ 5−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C5×C251⋊C5 |
| commutator, socle, cosocle | C5×C251 | C52 |
| Fitting | C25×C251 | C5 |
| prime radical | C5×C251⋊C5 | C5 |
| hypercenter | C25 | C251⋊C5 |
| hypocenter | C251 | 5−1+2 |
| LCS | G ▷ C5×C251 ▷ C251 | |
| UCS | C1 ◁ C5 ◁ C25 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
5^3,251|a^5=c,b^a=bc,d^b=d^1491279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31375, 13);