Finite Group DatabasebetaFinite Group Databasebeta| order | 31375 |
| automorphism | ? |
| homology | Abelianization (H1) = C125 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C251 ⋊ C125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C251 | C125 |
| prime radical | C251⋊C5 | C25 |
| cosocle | #20262474 | C5 |
| LCS | G ▷ C251 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
5^3,251|a^5=b,b^5=c,d^a=d^36,d^b=d^25,d^c=d^219127 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽251) |
| maximal normal subgroup of | AGL(1,𝔽251) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31375, 18);