Finite Group DatabasebetaFinite Group Databasebeta| order | 31375 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C52 |
| unambiguous semidirect product | C52⋊(C251⋊C5) |
| unambiguous semidirect product | C251⋊H(3,𝔽5) |
| unambiguous semidirect product | (C5×C251⋊C5)⋊C5 |
| Fitting | C52×C251 ⋊ C5 |
| Sylow | C251 ⋊ H(3,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C5×C251⋊C5 |
| commutator, socle, cosocle | C5×C251 | C52 |
| Fitting | C52×C251 | C5 |
| hypercenter | C52 | C251⋊C5 |
| hypocenter | C251 | H(3,𝔽5) |
| LCS | G ▷ C5×C251 ▷ C251 | |
| UCS | C1 ◁ C5 ◁ C52 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
5^3,251|b^a=bc,d^b=d^2191279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31375, 9);